Coding and modulation apparatus using non-uniform constellation

ABSTRACT

A coding and modulation apparatus and method are presented. The apparatus ( 10 ) comprises an encoder ( 11 ) that encodes input data into cell words, and a modulator ( 12 ) that modulates said cell words into constellation values of a non-uniform constellation. The modulator ( 12 ) is configured to use, based on the total number M of constellation points of the constellation, the signal-to-noise ratio SNR in dB and the channel characteristics, a non-uniform constellation from a group of constellations comprising one or more of predetermined constellations defined by the constellation position vector u1 . . . v, wherein v=sqrt(M)/2−1.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation of application Ser. No. 14/412,265,filed on Dec. 31, 2014, which is a National Stage Application ofInternational Application No. PCT/EP2013/063824, filed on Jul. 1, 2013,which claims the benefit of priority from EP Application No. 13164169.8,filed Apr. 17, 2013 and EP Application No. 12175587.0, filed Jul. 9,2012. The entire contents of each of the above applications areincorporated herein by reference in their entirety.

BACKGROUND

Field of the Disclosure

The present disclosure relates to a coding and modulation apparatus andmethod. Further, the present disclosure relates to a transmissionapparatus and method. Still further, the present disclosure relates to acomputer program and a non-transitory computer-readable recordingmedium.

Description of Related Art

Modern communications systems typically employ, among other elements, acoding and modulation apparatus (as part of a transmission apparatus)and a decoding and demodulation apparatus (as part of a receivingapparatus). The coding and modulation apparatus is often part of a socalled BICM (Bit Interleaved Coded Modulation) apparatus, whichgenerally comprises (at the transmitter side) a serial concatenation ofa FEC (Forward Error Correction) encoder, a bit interleaver, and amodulator, which uses spectral efficient modulation such as multilevelPAM (Pulse Amplitude Modulation), PSK (Phase Shift Keying), or QAM(Quadrature Amplitude Modulation). It should be noted that hereinafter,whenever QAM is mentioned it should be understood as a generally termcovering PAM, PSK and QAM.

BICM allows for good performance over both non-fading and fadingchannels due to the use of the interleaver and/or the FEC encoder. Ithas a reasonable decoding complexity as opposed to multilevel coding(MLC) coding schemes and is thus used frequently in communicationssystems, such as in all DVB systems, powerline communications (e.g.,Homeplug AV, DAB, LTE, WiFi, etc.).

Generally, the coding and modulation capacity, such as the BICM capacityin systems using a BICM apparatus, is considered as a target function,and it is desired to find optimum constellation points such that thiscapacity is maximized, often subject to a power normalization, i.e., theaverage power of the constellation points should be normalized to e.g.1.

The “background” description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventor(s), to the extent it is described in thisbackground section, as well as aspects of the description which may nototherwise qualify as prior art at the time of filing, are neitherexpressly or impliedly admitted as prior art against the presentdisclosure.

SUMMARY

It is an object to provide a coding and modulation apparatus and methodproviding an increased or even maximized coding and modulation capacity.It is a further object to provide a demodulation and decoding apparatusand method as well as a corresponding computer program for implementingsaid methods and a non-transitory computer-readable recording medium forimplementing said methods.

According to an aspect there is provided a coding and modulationapparatus comprising

-   -   an encoder that encodes input data into cell words, and    -   a modulator that modulates said cell words into constellation        values of a non-uniform constellation,        wherein said modulator is configured to use, based on the total        number M of constellation points of the constellation, the        signal-to-noise ratio SNR in dB and the channel characteristics,        a non-uniform constellation from a group of constellations        comprising one or more of the constellations defined by the        constellation position vector u_(1 . . . v), wherein        v=sqrt(M)/2−1, as described in detail in claim 1.

According to a further aspect there is provided a transmission apparatuscomprising

-   -   a coding and modulation apparatus as proposed herein that        encodes and modulates input data into constellation values,    -   a converter that converts said constellation values into one or        more transmission streams to be transmitted, and    -   a transmitter that transmits said one or more transmission        streams.

According to still further aspects corresponding methods, a computerprogram comprising program means for causing a computer to carry out thesteps of the coding and modulation method disclosed herein, when saidcomputer program is carried out on a computer, as well as anon-transitory computer-readable recording medium that stores therein acomputer program product, which, when executed by a processor, causesthe coding and modulation method disclosed herein to be performed areprovided.

Preferred embodiments are defined in the dependent claims. It shall beunderstood that the claimed methods, the claimed computer program andthe claimed computer-readable recording medium have similar and/oridentical preferred embodiments as the claimed apparatus and as definedin the dependent claims.

One of the aspects of the disclosure is that the constellation points ofthe used constellations are not located on a regular grid withequidistant symbols, but rather on optimized locations, dependent on thechannel characteristics, e.g., channel transition probabilities due toAWGN (Additive White Gaussian Noise), fading, etc. Further, the usedconstellation is selected dependent on the SNR (signal-to-noise ratio)and the desired total number of constellation points of the usedconstellation. A method how to find and optimize these non-uniformconstellations (in the following called NUCs) will be explained below.

It should be noted that to every M-QAM, one can also think of theunderlying sqrt(M)-PAM. Further, it should be noted that in otheraspects the group of constellations defined in the claims comprises lessconstellations, e.g. only constellations for non-fading channels, onlyconstellations for fading channels, only constellations for selectedvalues of M, only constellation for M-QAM or sqrt(M)-PAM and/orconstellations for less SNR values. In other words, less constellationsmay be contained in the group of constellations available for use by themodulator, i.e. the group of constellations available for use by themodulator may comprise one or more of the constellations defined in theclaims. Accordingly, the present disclosure is also directed to a codingand modulation apparatus and method that have a smaller group ofconstellations available for used and use (as explained above) and/orwhere less constellations are available for a particular value of M.

It should further be noted that for some values of M there are twooptions of constellations for fading channels and two options ofconstellations for non-fading channels provided for the same selectionparameters (e.g. for the same SNR value) among which the modulation canselect. These two options (referred to as 1. option and 2. option) arethe result of separate optimizations of the coding and modulationcapacity. Hence, for instance based on the desired capacity themodulator may select a constellation from the constellations accordingto the 1. option or the 2. option, wherein the constellations accordingto the 2. option generally provide a slightly higher capacity.

However, the constellation points of the QAM constellations consideredin this disclosure are not located on a regular grid with equidistantsymbols, but rather on optimized locations, dependent on the channelcharacteristics, e.g., channel transition probabilities due to AWGN,fading, etc.

It is to be understood that both the foregoing general description ofthe disclosure and the following detailed description are exemplary, butare not restrictive, of the disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the disclosure and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 shows an embodiment of a coding and modulation apparatusaccording to the present disclosure,

FIG. 2 shows an embodiment of a transmission apparatus according to thepresent disclosure,

FIG. 3 shows an embodiment of a communications system according to thepresent disclosure,

FIG. 4 shows a regular 4-QAM constellation as a simple example for aconstellation,

FIG. 5A shows a diagram depicting an integrant of the 1-dimensional BICMcapacity function at 30 dB SNR,

FIG. 5B shows a diagram depicting an integrant of the 1-dimensional BICMcapacity function at 10 dB,

FIG. 6A shows a 8-PAM non-uniform constellation,

FIG. 6B shows a 64-QAM non-uniform constellation,

FIG. 7 shows a constellation for a 64-QAM non-uniform constellationgenerally defining the constellation points, and

FIG. 8 shows a diagram illustrating the performance of non-uniformN²-QAM constellations.

DESCRIPTION OF THE EMBODIMENTS

Referring now to the drawings, wherein like reference numerals designateidentical or corresponding parts throughout the several views, FIG. 1shows an embodiment of a coding and modulation apparatus 10 according tothe present disclosure. It comprises an encoder 11 that encodes inputdata into cell words, and a modulator 12 that modulates said cell wordsinto constellation values of a non-uniform constellation. Said modulator12 is configured to use (and, preferably, select in advance), based onthe total number M of constellation points of the constellation, thesignal-to-noise ratio SNR in dB and the channel characteristics, anon-uniform constellation from a group of constellations comprisingpredetermined constellations defined by the constellation positionvector u_(1 . . . v), wherein v=sqrt(M)/2−1. These predeterminedconstellations will be derived and shown below.

In other embodiments of the coding and modulation apparatus 10additional elements may be provided, such as a BCH encoder, an LCPCencoder, a bit interleaver and/or a demultiplexer (for demultiplexingbits of encoded data into the cell words). Some or all of these elementsmay separate elements or may be part of the encoder 11. For instance, aBICM device as conventionally used in the transmission apparatus of aDVB system may be used as coding and modulation apparatus 10.

FIG. 2 shows an embodiment of a transmission apparatus 20 according tothe present disclosure comprising a coding and modulation apparatus 21(referenced by 10 in FIG. 1) as proposed herein that encodes andmodulates input data into constellation values, a converter 22 thatconverts said constellation values into one or more transmission streamsto be transmitted, and a transmitter 23 that transmits said one or moretransmission streams. In an exemplary embodiment the converter 22 maycomprise one or more elements like a time, cell and/or frequencyinterleaver, a frame builder, an OFDM modulator, etc., as e.g. describedin the various standards related to DVB. The constellations and theconstellations values are generally predetermined and e.g. stored in aconstellations storage 24 or retrieved from an external source.

In other embodiments of the transmission apparatus 20 addition elementsmay be provided, such as an input processing unit, a frame building unitand/or an OFDM generation unit as e.g. conventionally used intransmission apparatus of a DVB system.

FIG. 3 shows an embodiment of a communications system 30 according tothe present disclosure comprising one (or more) transmission apparatus20 (Tx) as shown in FIG. 2 and one or more receiving apparatus 40, 40′(Rx).

A receiving apparatus 40 generally comprises a receiver 41 that receivesone or more transmission streams, a deconverter 42 that deconverts thereceived one or more transmission streams into constellation values, anda demodulation and decoding apparatus 43 that demodulates and decodessaid constellation values into output data. The demodulation anddecoding apparatus 43 generally comprises a demodulator 44 fordemodulating constellation values of a non-uniform constellation intocell words, and a decoder 45 for decoding cell words into output datawords, wherein based on the total number M of constellation points ofthe constellation, the signal-to-noise ratio in dB and the channelcharacteristics, a non-uniform constellation is used from the group ofconstellations comprising the same predetermined constellations as usedin the coding and modulation apparatus 10.

The preferred demodulation and decoding considers soft values as opposedto hard decided values (0 and 1). Soft values represent the continuouslydistributed received values (possibly after A/D conversion includingquantization) by more than two states (as in the case of binary (hard)decision). The reason is that for hard decision, the NUCs are generallynot optimal. Nowadays, BICM receivers typically are soft receiversanyway.

Generally, data (e.g. communications data, broadcast data, etc.) shallbe transmitted from a transmission apparatus 20 to one or more of saidreceiving apparatus 40 over a transmission channel 50, 50′. Thetransmission channel 50, 50′ can be unicast channel, multicast channel,a broadcast channel and may be employed as one-directional orbi-directional channel (i.e. having a return channel from the receivingapparatus to the transmission apparatus).

In an embodiment the modulator 12 is configured to select and use anon-uniform constellation based on the total number M of constellationpoints of the constellation, the required signal-to-noise ratio SNR forerror free decoding in dB and the channel characteristics. Inbroadcasting applications the constellation is generally not selecteddependent on the SNR in the receiver, but dependent on the SNR that isrequired for error free decoding with a used channel code (if a code isused, for example LDPC codes in case of DVB 2^(nd) generationtransmission systems) for an expected channel characteristic, e.g.,static reception or multipath fading.

The total number M of constellation points is generally selectedaccording to the desired payload throughput jointly with the code rateof the FEC encoder. The SNR for error free decoding for typical channelcharacteristic is generally known, e.g. by simulation. In broadcastingthe channel characteristics of the receivers are not known, i.e. acompromise is selected. For instance, in broadcasting for each code rateof the FEC encoder one non-uniform constellation is selected, optimizedfor an SNR that is a compromise for all channel characteristics.

The transmitter generally targets a certain scenario. For instance, abroadcast transmission over cable or satellite considers the channel tobe just a non-fading AWGN (appropriate channel model), while aterrestrial broadcaster typically considers the channel to be a fadingchannel, e.g. with Rayleigh distribution, as several echoes are usuallyreceived.

In another embodiment the modulator 12 is configured to adaptivelyselect and use a non-uniform constellation based on the total number Mof constellation points of the constellation, the signal-to-noise ratioSNR in dB and the channel characteristics, wherein said signal-to-noiseratio SNR in dB and channel characteristics are received from areceiving device 40 to which data shall be transmitted. Such an adaptiveselection of the constellation is generally only possible with a returnchannel in unicast environments. A non-uniform constellation may beadapted e.g. in time and/or frequency domain, e.g. for different OFDMsubcarriers.

Depending on the SNR the optimum value for M and the code rate of theFEC encoder can be selected, which offers the highest throughput(equivalent to C_(B)). In other words, for a large SNR a high value of Mis selected leading to a high data throughput (and vice versa).

The channel characteristics describe the statistical properties of thechannel, e.g., the extent of the multipath propagation of thetransmission channel between transmitter and receiver. If the channel ischaracterized by no multipath propagation, corresponding to the AWGNchannel, the required SNR for error free decoding is relatively low,i.e. the NUC has to be selected accordingly for optimum performance. Ifthe transmission channel is characterized by strong multipathpropagation, the required SNR for error free reception is largercompared to a channel without multipath propagation, i.e. a NUCoptimized for higher SNR has to be used. Further, the NUCs should beoptimized taking the fading characteristics into account, as will bediscussed below.

As mentioned above, the number M of the constellation points of theconstellations is selected according to the desired payload throughput.Larger values of M allow for higher data throughput, but require alarger SNR for error free reception. This is further influenced by thecode rate of the FEC encoder, if any FEC encoder is used.

Another explanation (which is closely related to the optimization taskof the present disclosure) is that for each SNR, optimizedconstellations are proposed for different M. The optimization target isthe BICM capacity. For an expected SNR, say 15 dB of SNR should beguaranteed, M is chosen, for which the respective optimized NUC yieldsthe largest BICM capacity. As a general rule it holds that for low SNR alow value of M should be selected and vice versa. But from a theoreticalpoint of view, it turns out that high M is generally optimum, e.g.,choosing M=4096 or M=1024 is preferred, because even for low SNR, theoptimized NUC will “look (almost) like” a constellation with effectivelysmaller M, as several points will overlap. However, modulation anddemodulation complexity increase with increasing M, so a tradeoff has tobe considered.

As mentioned above known communications systems often employ among otherblocks a so called BICM apparatus which may also be used as coding andmodulation apparatus according to the present disclosure. The maximumpossible capacity over a BICM apparatus is described by the BICMcapacity C_(B):

$\begin{matrix}{{C_{B} = {{\sum\limits_{i = 0}^{m - 1}\;{E_{b,r_{k}}\;\left\lbrack {\log_{2}\frac{\sum\limits_{x_{l} \in {\mathbb{X}}_{b}^{i}}\;{p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}}{p\left( r_{k} \right)}} \right\rbrack}} = {\int_{r_{k} \in {\mathbb{C}}}{\sum\limits_{i = 0}^{m - 1}\;{\sum\limits_{b = 0}^{1}\;{\sum\limits_{x_{l} \in {\mathbb{X}}_{b}^{i}}{{\frac{1}{M} \cdot {p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}}\log_{2}\frac{\sum\limits_{x_{l} \in {\mathbb{X}}_{b}^{i}}\;{p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}} \right)}}{\frac{1}{M} \cdot {\sum\limits_{x_{l}^{\prime} \in {\mathbb{X}}}\;{p\left( {\left. r_{k} \middle| s_{k} \right. = x_{l}^{\prime}} \right)}}}{dr}_{k}}}}}}}},} & (1)\end{matrix}$where I denotes the i-th bit label of the constellation point, and m isthe total number of bits/QAM symbol point. Altogether the QAMconstellation consists of M=2^(m) constellation points, each assigned aparticular bit label (00 . . . 00, 00 . . . 01, . . . , 11 . . . 11). In(1), E[.] denotes expectation operator, p(r_(k)) is the probabilitydensity function (pdf) of the received symbols, s_(k) is the transmittedsymbol according to a particular bit label, k is the discrete time (orsubcarrier index in case of OFDM modulation), x₁ is a particular symbolof the set of all constellation symbols, this set being denoted by

(=symbol alphabet, with cardinality M=2^(m)).

p(r_(k)|s_(k)=x₁) is the likelihood function (transitionprobability—defined by the channel characteristics) that r_(k) isreceived given the fact that s_(k)=x₁ was transmitted. The subset

_(b) ^(i) includes all symbols from

, where the i-th bit label is b (either b=0 or b=1).

As seen in (1), C_(B) is a 2-dimensional integral. If onlyconstellations are considered that can be split into two 1-dim. PAMconstellations, it is easy to see thatC _(B)(2-dim.)=2×C _(B)(1-dim.)  (2)

All investigated channels here include AWGN (only or after the fadingchannel). This can be described by the signal-to-noise ratio SNR,typically in dB:SNR=10*log₁₀(E _(s)/σ²),  (3)where E_(s) is the average symbol power of the QAM constellation(typically normalized to 1), and σ² is the variance (=power) of theadditive white Gaussian noise (which is assumed to be of zero-mean).

In (2), the 1-dimensional consideration for C_(B) (1-dim.) uses an N-PAMconstellation, which has only half the symbol power, if just theprojection on the in-phase or quadrature-phase, respectively, is taken.However, if again a power normalization to 1 is considered, the noisevariance by a factor of 2 is increased. Thus, to be more precise, thetarget function for the optimization process considered according to thepresent disclosure is given byC _(B)(2-dim. at SNRx)=2×C _(B)(1-dim. at SNRx/2),  (4)where the 1-dimensional PAM has normalized power 1, thus just half theSNR (here, in absolute values, i.e. not in dB) as explained above. The1-dimensional BICM capacity is also computed according to (1), where the2-dimensional integral becomes a 1-dimensional integral with r_(k)∈

,

being the set of real numbers.

This equation (4) is optimized, given all degrees of freedom, namely theconstellation points of the underlying 1-dim. constellation, subject tothe power constraint, i.e.,

$\begin{matrix}{\mathcal{P}_{x} = {{E_{s_{k}}\left\lbrack {s_{k}}^{2} \right\rbrack} = {{E_{x_{l}}\left\lbrack {x_{l}}^{2} \right\rbrack} = {{\frac{1}{M}{\sum\limits_{l = 0}^{M - 1}\;{x_{l}}^{2}}}\overset{!}{=}1}}}} & (5)\end{matrix}$

For example, a regular 4-QAM consists of constellation points (e^(jπ/4),e^(j7π/4), e^(3π/4), e^(j5π/4)), as can be seen in FIG. 4. The averagesymbol power is 1 (all symbols are located on unit circle here). Theabove symbol vector (e^(jπ/4), e^(j7π/4), e^(3π/4), e^(j5π/4)) is to beunderstood such that the first entry (e^(jπ/4)) belongs to the bitvector 00, the second entry (e^(j7π/4)) to 01 and so on, i.e. theentries belong to bit vectors with increasing values, where the firstbit position is the most significant bit (MSB) and the last one theleast significant bit (LSB). This 4-QAM is a particular case of anN²-QAM, with N=2. Note that this definition (of being an N² QAM) doesnot only require N² being a square number (N²=2²), but also that theconstellation is symmetrical and can be described by two independentN-PAM constellations, here a 2-PAM: the in-phase component (real-part ofthe complex symbols) is a 2-PAM with symbol vector (1/sqrt(2),−1/sqrt(2)) and describes the 1^(st) bit of the 4-QAM, whereas thequadrature-phase component (imaginary-part of the complex symbols) isthe same 2-PAM, this time describing the 2^(nd) bit of the 4-QAM. Notefurther that the decomposition of the N²-QAM into two N-PAMs is onlypossible if the bit labeling is according to binary reflected Graymapping, which is typically applied (e.g. in DVB-systems).

The above example can be extended to higher order N²-QAMs, with M>2.Then the underlying N-PAM describes for one component the 1^(st),3^(rd), 5^(th) and so on bit label, while for the other component itdescribes the 2^(nd), 4^(th), 6^(th) and so on label.

Constellation shaping is generally known and has a long history. Only inrecent years, constellations were investigated which maximize the BICMcapacity C_(B). In [6], the authors propose an heuristic approach tomaximize C_(B) by forcing the underlying PAM to approach a Gauss-likeform (as is well known from Shannon's capacity theorem, the optimumconstellation over the AWGN channel should have a Gaussian distribution;note that this means that there is an infinite number of continuouslydistributed input signals, having a Gaussian distribution, i.e., symbolswith small power should occur more frequently than symbols with largepower). There is no proof that this maximizes C_(B), indeed those NUCsdesigned according to this method do not maximize C_(B). The resultingNUCs are in general no N² NUCs, i.e., a 2-dimensional NUC was optimized,not the underlying PAM. However, in N. Muhammad, “Coding and modulationfor spectral efficient transmission”, Ph.D. dissertation, UniversitätStuttgart, Institut für Nachrichtenübertragung, Pfaffenwaldring 47,70569 Stuttgart, Germany, June 2006, the first time constellations havebeen directly optimized with respect to the target function C_(B). Forthis method two differences to the current method occur:

-   -   M-NUCs were proposed for M=8, 16, and 32. No higher order NUCs        were investigated, as the optimization becomes very time        consuming and the optimization algorithms became numerically        unstable.    -   The optimization algorithm was a hand-written gradient search        algorithm, where both the BICM capacity and the gradient thereof        consisted of improper integrals. No special care about either        the numerical solution of the improper integral or the        problematic integrants was considered. This consideration of        these two issues is fundamental to obtain results for high order        constellations, such as 1 k (i.e. 1024) NUC.

As described above, two problems arise when solving the optimization:

a) improper integral: integration border selection; and

b) integrant.

With respect to problem a) (improper integral: integration borderselection), as seen in eq. (1), the BICM capacity involves an integralfrom −infinity to +infinity (=improper integral). Any numerical solutionof this integral has to consider finite integration borders such as from−b to +b, with b sufficiently large. Matlab provides several functionsfor numerical integration, even for improper integrals, such as thefunction “quad”, which internally optimizes the appropriate integrationborders b. However, it has been observed that even these functions yieldnumerical instabilities and do not end up with the correct integral.

It can be observed that the integrant in (1) approaches 0 if thevariable r_(k) is sufficiently large (b→lnf). So a naïve approach wouldbe to stepwise increase the variable r_(k), until the integrant fallsbelow a certain threshold (say 10⁻³⁰⁰ or if it even becomes exactly 0)and chose this value for the integration border b. However, it hasfurther been observed that the integrant can take on very small valueseven before it converges to 0 for large variables, as can be seen in thetwo examples depicted in FIGS. 5A and 5B: the plot shown in FIG. 5B isthe integrant of the 1-dimensional BICM capacity function, if a regular32-PAM is used, at 10 dB SNR, while the plot shown in FIG. 5A 30 dB isconsidered.

Note that for 30 dB, many very small integrant values occur in theinterval [−2,2] and any optimized integration border would be misleadingin this interval. Thus, it is proposed to find the optimum (=numericallycorrect) integration border b as follows:

i) start with a large positive value S, iteratively reduce the value bydecrements D, compute the integrant with this value as variable r_(k),until the first non-zero value of the integrant is computed. If nonon-zero integrant can be found before r_(k)=0, start again with alarger initial value S (say 10 times larger than before) and reduce D(say by factor of 10) to have a larger search interval and a finergranularity.ii) As this search is time consuming, it is proposed to adjust theinitial value S and the decrement D according to the SNR. If σ² is thenoise variance of the 1-dimensional mapping (see eq. (3)), then as agood compromise S=4000*σ² and D=50*σ² has been chosen.

With respect to problem b) (integrant) it has further been observed thatthe integrant of the BICM capacity integral can cause numericalinstabilities for large SNR values. As can be seen in eq. (1), theintegrant consists of sums, including terms such asx*log(x),x*log(1/x), or x*1/log(x).

The value of x is e.g. the transition probability p(r_(k)|s_k=x₁), or apdf or includes parts thereof. The values of x become increasingly small(even approaching 0) if the SNR is very large, as the pdfs typicallycorrespond to Gaussian distributions. Thus, the following limits mightoccur:lim_({x) _(→) _(0}) x*log(x),lim_({x) _(→) _(0}) x*log(1/x), or lim_({x)_(→) ₀ }x*1/log(x).

Note that in theory, each limit converges to 0 (see l'Hospital's rule),but in a numerical computation, values such as + or − infinite or NaN(“not a number”) will occur. Thus, the following is proposed: during thecomputation of each element (i.e., each addend in the integrant of (1)),the value has to be checked if it is finite (otherwise infinite or NaN),and replace it by 0 in case it is not finite. Only this way, reliableintegration results can be obtained.

With the above considerations, N²-NUCs have been optimized as oneembodiment with N² being 16, 64, 256, 1024 (1 k), 4 k, 16 k, 64 k, 256 kand 1024 k. This means, the target function C_(B) of the underlying1-dimensional PAM is used and the degrees of freedom (the real-valuedconstellation points of the PAM) are optimized. Note that the PAM hasonly N=sqrt(N²) degrees of freedom (e.g. a 64-NUC is based on an 8-PAM).Due to symmetry, the negative constellation values are the same as theirpositive counterparts, such that only N/2 degrees of freedom remain.Finally, one more degree of freedom is lost due to the powernormalization (5). The 64-NUC can thus be optimized by considering only3 degrees of freedom (“dof”, i.e., optimization variables).

The presented optimization is preferably based on the Matlab's fminconfunction for constrained nonlinear optimization: the target function isthe BICM capacity, the constraints are as follows:

-   -   all dof (degrees of freedom)>0;    -   all dof need to fulfill the power normalization, when the N-PAM        is created based on them;    -   the dof must occur in increasing order.

The function fmincon requires an initial set of dof, where the valueswere taken from a regular, i.e. uniform constellation, but a randommutation was applied on them. It is to be noted that the resultingvalues should still be in increasing order, otherwise the Gray bitlabeling is not fulfilled anymore. The NUCs will be described by theirdegrees of freedom, e.g., a 64-NUC optimized for the AWGN channel atSNR=11.5 dB yields the following values (optimized degrees of freedom):

-   -   2.2794 4.6229 7.5291.        This means that the positive constellation values are    -   1 2.2794 4.6229 7.5291        (the 1 was redundant, due to the power normalization, which will        be applied in the end). The underlying 1-dim. 8-PAM NUC is thus        described by the symbol vector    -   (1.6405 1.0073 0.2179 0.4967 −1.6405 −1.0073 −0.2179 −0.4967),        where the values are already normalized to unit average power.

As described before, the first entry (1.6405) corresponds to the bitlabel 000, the next one (1.0073) to 001 and so on. The 2-dim. 64-NUC isthen obtained by symmetry, where both in-phase and quadrature-phasecomponent of the NUC are based on the 8-PAM NUC.

FIG. 6A shows a 8-PAM NUC while FIG. 6B shows a 64-QAM NUC. The bitlabels are given in integer numbers (000→0, 001→1, 010→2 and so on).

The creation of the 2-dim. NUC based on the optimized degrees of freedomwill be explained in more detail below.

Since the performance of NUCs depends on the SNR value they areoptimized for, a thorough selection is preferably carried out dependingon the (FEC) code rate to achieve optimum performance. If the channelcharacteristics are known, the required SNR value for FEC convergencecan be determined by simulation. Then the NUC that has been optimizedfor this SNR value is chosen for best performance. If the SNR at thereceiver is lower than this SNR decoding threshold, the constellation isnot optimal. However, this is no drawback, since the BICM capacity istoo low for successful decoding anyhow. On the other hand if the SNR atthe receiver is clearly higher than the decoding threshold, a sufficientamount of BICM capacity for successful decoding is available, eventhough the NUC is suboptimal for this SNR range. Therefore, the NUCneeds to be optimized for the SNR value at the waterfall region (i.e.,decoding threshold for (quasi-) error free decoding) of the FEC. As theSNR value of the waterfall region depends on the code rate of the FEC, adifferent NUC is selected for each code rate.

The SNR value for (quasi-) error free decoding also depends on thechannel characteristics of the receiver. For instance the required SNRfor error free decoding of the DVB-T2 LDPC code in the AWGN channel is0.8 dB, whereas 2.5 dB are required in the Rayleigh P1 multipathchannel. The selected NUC for each code rate is thus not optimal in allchannel environments and a tradeoff is necessary in a broadcastingenvironment that suits all (or most) users in the network. In apoint-to-point network with return channel, the optimal NUC may beselected based on the measured channel characteristics in the receiver.

Currently, there exist no optimized constellations for fading channels.If the transmitter has no channel state information (CSI), but thereceiver has perfect CSI (due to, e.g., pilot-based channel estimation),then the average BICM is the target function, which needs to beoptimized for NUCs designed for fading channels. If the magnitude of thefading value for one QAM symbol is denoted as h (e.g. for a particulartime instant and/or a particular subcarrier in case of OFDM), then theinstantaneous BICM capacity is called C_(B)(h) and given acc. to eq.(1). Note that the pdfs and transition probabilities in (1) are nowdifferent from the pure AWGN channel. E.g. in the AWGN case, thelikelihood function p(r_(k)|s_(k)=x₁) was given by a Gaussiandistribution with zero-mean and variance σ². Now, for fading with thevalue h, the distribution is still Gaussian with zero-mean, but withinstantaneous variance σ²/h².

A good model for the fading statistics is given by a Rayleighdistribution of the fading magnitude h. Thus, the pdf of h is:p(h)=h/σ _(h) ²*exp(−h ²/(2*σ_(h) ²)),  (6)where σ_(h) ² is the variance of the Rayleigh distribution. For apassive channel, i.e. one which on average neither attenuates normagnifies the signal, σ_(h) ²=½. This means, that the average SNR over afading channel is the same as of a non-fading channel.

Now, the average BICM capacity over many channel realizations is givenbyC _(B)=∫₀ ^(∞) p(h)*Cb(h)dh,  (7)i.e., the instantaneous BICM capacity as a function of h has to bemultiplied by the pdf of h (see (6)) and integrated over all possiblefading magnitudes (0 . . . infinity).

Again, an improper integral has to be solved. This time, the integrantof (7) converges to 0 due to the pdf of h. It was found that asufficiently large upper limit for the integral in (7) is given by 38,independent of the instantaneous capacity C_(B)(h). This enables fasteroptimization of (7). Results will be shown below for N²-NUCs, N²=16, 64,256, 1024 (1 k), 4096 (4 k) and 16384 (16 k).

The same principle regarding the selection of the NUC that has beendescribed for static channels also holds for receivers experiencingfading channels, e.g., portable or mobile receivers. But since in fadingchannels the SNR in the receiver is varying due to the fading effect ofthe channel, the NUC cannot always operate at the optimum SNR. Ingeneral, the NUCs optimized for the fading channel perform bettercompared to the NUCs optimized for the non-fading channel when used atSNR values for which they are initially not optimized for, i.e. theyperform better over broader SNR regions. Moreover, it was found that theNUCs optimized for the Rayleigh fading channel are good for most fadingchannels, e.g., with Rice distribution, with more than one echocomponent (e.g. TU6 channel) or with time- and frequency-selectivefading with correlation. This is because the optimization considers theaverage of several channel instances/realizations.

In the following some more explanation is provided regarding thedefinition of the non-uniform QAM constellations. Each input cell word(y_(0,q) . . . y_(m-1,q)) (i.e. provided to the modulator) shall bemodulated using a non-uniform QAM constellation to give a constellationpoint z_(q) prior to normalization, where m corresponds to the number ofbits per QAM symbol m=log₂(M). It should be noted that the parameter qused here for discrete time or subcarrier index corresponds to theparameter k as used in the above. The exact values of the real andimaginary components Re(z_(q)) and Im(z_(q)) for each combination of therelevant input bits y_(0 . . . m-1,q) are given in the following tablesfor the various constellation sizes depending on the NUC position vectoru_(1 . . . v), which defines the constellation point position of thenon-uniform constellation. The length of the NUC position vector u isdefined by

$v = {\frac{\sqrt{M}}{2} - 1.}$

In one example, the corresponding constellation point z_(q) for a 64-QAMNUC defined by the NUC position vector (u_(1 . . . 3))=(2,5,6) and theinput cell word (y_(0,q) . . . y_(m-1,q)=(100111) is Re(z_(q))=−u₂=−5and Im(z_(q))=u₁=2. The complete constellation for this NUC positionvector is shown in FIG. 7 with exemplary input cell words marked at thecorresponding constellation points.

The resulting constellation mapping (also called labeling) for thenon-uniform constellations follows a binary reflected Gray-Mapping(labeling), i.e. neighboring constellation points differ in only onebit. The power of the constellation points z_(q) is normalized such thatthe expectation value of the normalized constellation point f_(q) equals1, i.e. E(|f_(q)|²)=1. For example, the normalized constellation valuef_(q) of a uniform 16-QAM constellation results by

$f_{q} = {\frac{z_{q}}{\sqrt{10}}.}$FIG. 8 shows a diagram illustrating the performance of non-uniformN²-QAM constellations.

The following tables define the constellation position vectors (prior topower normalization) as well as the bit labelling of the data cell wordsto the constellation points.

Constellation Mapping for Real Part of 16-QAM

y_(0,q) 1 1 0 0 y_(2,q) 0 1 1 0 Re(z_(q)) −3 −1 1 3 Uniform −u₁ −1 1 u₁NUC

Constellation Mapping for Imaginary Part of 16-QAM

y_(1, q) 1 1 0 0 y_(3, q) 0 1 1 0 Im(z_(q)) −3 −1 1 3 Uniform −u₁ −1 1u₁ NUC

Constellation Mapping for Real Part of 64-QAM

y_(0, q) 1 1 1 1 0 0 0 0 y_(2, q) 0 0 1 1 1 1 0 0 y_(4, q) 0 1 1 0 0 1 10 Re(z_(q)) −7 −5 −3 −1 1 3 5 7 Uniform −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ NUC

Constellation Mapping for Imaginary Part of 64-QAM

y_(1, q) 1 1 1 1 0 0 0 0 y_(3, q) 0 0 1 1 1 1 0 0 y_(5, q) 0 1 1 0 0 1 10 Im(z_(q)) −7 −5 −3 −1 1 3 5 7 Uniform −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ NUC

Constellation Mapping for Real Part of 256-QAM

y_(0, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(2, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(4, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(6, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Re(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11 13  15  Uniform −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇NUC

Constellation Mapping for Real Part of 256-QAM

y_(1, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(3, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(5, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(7, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Im(z_(q)) −15 −13 −11 −9 −7 −5 −3 −1 1 3 5 7 9 11 13  15  Uniform −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇NUC

Constellation Mapping for Real Part of 1024-QAM

Y_(0, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 0 0 0 0 0 0 0 0 1 1 11 1 1 1 1 y_(4, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6, q) 0 0 1 1 1 10 0 0 0 1 1 1 1 0 0 y_(8, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q))−31  −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅−u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUCY_(0, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2, q) 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 y_(4, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6, q) 0 0 1 1 1 10 0 0 0 1 1 1 1 0 0 y_(8, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) 13 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅ u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅ NUC

Constellation Mapping for Imaginary Part of 1024-QAM

y_(1, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 0 0 0 0 0 0 0 0 1 1 11 1 1 1 1 y_(5, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7, q) 0 0 1 1 1 10 0 0 0 1 1 1 1 0 0 y_(9, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q))−31  −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅−u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUCy_(1, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(3, q) 1 1 1 1 1 1 1 1 0 0 00 0 0 0 0 y_(5, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7, q) 0 0 1 1 1 10 0 0 0 1 1 1 1 0 0 y_(9, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 13 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂  u₃  u₄  u₅ u₆  u₇  u₈  u₉  u₁₀  u₁₁  u₁₂  u₁₃  u₁₄ u₁₅ NUC

Constellation Mapping for Real Part of 4096-QAM

Y_(0, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 y_(4, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(6, q) 0 0 0 0 1 11 1 1 1 1 1 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 01 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Re(z_(q)) −63 −61 −59 −57 −55 −53 −51 −49−47 −45 −43 −41 −39 −37 −35 −33 Uniform −u₃₁ −u₃₀ −u₂₉ −u₂₈ −u₂₇ −u₂₆−u₂₅ −u₂₄ −u₂₃ −u₂₂ −u₂₁  −u₂₀  −u₁₉  −u₁₈  −u₁₇  −u₁₆  NUC Y_(0, q) 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1y_(4, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(6, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Re(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13−11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉   −u₈   −u₇  −u₆   −u₅  −u₄  −u₃  −u₂  −u₁  −1 NUC Y_(0, q) 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 y_(2, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(4, q) 0 0 0 0 0 0 00 1 1 1 1 1 1 1 1 y_(6, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(8, q) 0 01 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0Re(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂ u₃  u₄  u₅  u₆  u₇  u₈  u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC Y_(0, q) 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 y_(2, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0y_(4, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(6, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(8, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(10, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Re(z_(q)) 33 35 37 39 41 43 45 47 49 51 53 55 57 5961 63 Uniform  u₁₆  u₁₇  u₁₈  u₁₉  u₂₀  u₂₁  u₂₂  u₂₃  u₂₄  u₂₅ u₂₆ u₂₇u₂₈ u₂₉ u₃₀ u₃₁ NUC

Constellation Mapping for Imaginary Part of 4096-QAM

y_(1, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 y_(5, q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(7, q) 0 0 0 0 1 11 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 01 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −63 −61 −59 −57 −55 −53 −51 −49−47 −45 −43 −41 −39 −37 −35 −33 Uniform −u₃₁ −u₃₀ −u₂₉ −u₂₈ −u₂₇ −u₂₆−u₂₅ −u₂₄ −u₂₃ −u₂₂ −u₂₁  −u₂₀  −u₁₉  −u₁₈  −u₁₇  −u₁₆  NUC y_(1, q) 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(3, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1y_(5, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(7, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Im(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13−11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉  −u₈  −u₇ −u₆  −u₅  −u₄  −u₃  −u₂  −u₁  −1 NUC y_(1, q) 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 y_(3, q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(5, q) 0 0 0 0 0 0 0 01 1 1 1 1 1 1 1 y_(7, q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(9, q) 0 0 11 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0Im(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1  u₁  u₂ u₃  u₄  u₅  u₆  u₇  u₈  u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC y_(1, q) 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 y_(3, q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0y_(5, q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(7, q) 0 0 0 0 1 1 1 1 1 1 11 0 0 0 0 y_(9, q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(11, q) 0 1 1 0 0 11 0 0 1 1 0 0 1 1 0 Im(z_(q)) 33 35 37 39 41 43 45 47 49 51 53 55 57 5961 63 Uniform  u₁₆  u₁₇  u₁₈  u₁₉  u₂₀  u₂₁  u₂₂  u₂₃  u₂₄  u₂₅ u₂₆ u₂₇u₂₈ u₂₉ u₃₀ u₃₁ NUC

In the following the definition of the NUC position vectors obtained byuse of the above described approach is provided. The signal-to-noiseratio (SNR) is always denoted in dB and corresponds to the average SNRin case of fading channels.

a1) 16-QAM or 4-PAM for a Non-Fading Channel (1. Option)

SNR 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 u₁ 1.00011.0001 1.0002 1.1550 1.6201 1.9580 2.2633 2.5594 2.8411 3.0980 3.33573.5294 3.6712 3.7520 SNR 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.512.0 12.5 13.0 13.5 u₁ 3.7812 3.7480 3.6736 3.5998 3.5184 3.4446 3.38183.3239 3.2786 3.2407 3.2109 3.1793 3.1581 3.1390 SNR 14 14.5 15.0 15.516.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 u₁ 3.1219 3.1078 3.09643.0819 3.0774 3.0665 3.0579 3.0528 3.0485 3.0423 3.0411 3.0333 3.0521a2) 16-QAM or 4-PAM for a Fading Channel (1. Option)

SNR 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 u₁ 1.62891.8484 2.0415 2.2247 2.3853 2.5335 2.6736 2.7962 2.8980 2.9832 3.05933.1169 3.1616 3.1973 SNR 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.512.0 12.5 13.0 13.5 u₁ 3.2180 3.2334 3.2427 3.2473 3.2477 3.2463 3.24363.2388 3.2312 3.2291 3.2224 3.2149 3.2129 3.2055 SNR 14 14.5 15.0 15.516.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 u₁ 3.2036 3.1976 3.19533.1917 3.1854 3.1853 3.1803 3.1799 3.1761 3.1712 3.1715 3.1721 3.1711a3) 16-QAM/4-PAM for a Non-Fading Channel (2. Option)

SNR/u 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 u₁ 1.0001 1.0001 1.00021.155 1.6201 1.958 2.2633 2.5594 2.8411 3.098 3.3357 3.5294 3.6712 3.752SNR/u 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 u₁ 3.7812 3.7483.6736 3.5998 3.5184 3.4446 3.3818 3.3239 3.2786 3.2407 3.2109 3.17933.1581 3.139 SNR/u 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.5 20 u₁3.1219 3.1078 3.0964 3.0819 3.0774 3.0665 3.0579 3.0528 3.0485 3.04233.0411 3.0333 3.0521a4) 16-QAM/4-PAM for a Fading Channel (2. Option)

SNR 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 u₁ 1.6289 1.8484 2.04152.2247 2.3853 2.5335 2.6736 2.7962 2.898 2.9832 3.0593 3.1169 3.16163.1973 SNR 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 u₁ 3.2183.2334 3.2427 3.2473 3.2477 3.2463 3.2436 3.2388 3.2312 3.2291 3.22243.2149 3.2129 3.2055 SNR 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 19 19.520 u₁ 3.2036 3.1976 3.1953 3.1917 3.1854 3.1853 3.1803 3.1799 3.17613.1712 3.1715 3.1721 3.1711b1) 64-QAM or 8-PAM for a Non-Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0000 1.0022 1.0009 1.19451.4265 1.7169 2.0784 2.4886 2.8098 2.9798 3.0657 3.0895 3.0744 u₂ 2.67993.6839 3.7714 3.5638 3.6893 3.9984 4.4060 4.8482 5.2018 5.4093 5.51005.4881 5.3864 u₃ 3.4087 3.6839 3.7779 4.6322 5.4024 6.2400 7.1114 7.92628.4762 8.7005 8.7024 8.4935 8.1750 SNR 18 19 20 21 22 23 24 25 26 27 2829 30 u₁ 3.0557 3.0409 3.0309 3.0244 3.0180 3.0140 3.0153 3.0107 3.00012.7744 2.2837 3.0137 1.9278 u₂ 5.2889 5.2157 5.1647 5.1260 5.0979 5.07665.0685 5.0403 5.0254 4.5265 3.3188 5.1307 3.2632 u₃ 7.8949 7.6816 7.52657.4114 7.3213 7.2517 7.2083 7.1286 7.1277 6.6760 5.0386 6.6178 4.4151b2) 64-QAM or 8-PAM for a Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0353 1.1062 1.2092 1.34511.5409 1.8112 2.1208 2.3945 2.6067 2.7560 2.8505 2.9120 2.9496 u₂ 2.82062.9015 3.0799 3.2980 3.5826 3.9386 4.3237 4.6577 4.9074 5.0773 5.16745.2201 5.2393 u₃ 3.4534 3.9220 4.4154 4.9297 5.5069 6.1594 6.8108 7.34757.7177 7.9488 8.0398 8.0680 8.0538 SNR 18 19 20 21 22 23 24 25 26 27 2829 30 u₁ 2.9751 2.9907 3.0032 3.0055 3.0126 3.0124 3.0136 3.0165 3.01563.0158 3.0160 3.0180 3.0183 u₂ 5.2491 5.2493 5.2489 5.2365 5.2375 5.22475.2182 5.2165 5.2098 5.2070 5.2040 5.2036 5.1995 u₃ 8.0217 7.9849 7.95287.9035 7.8862 7.8443 7.8194 7.8046 7.7839 7.7661 7.7620 7.7569 7.7566b3) 64-QAM/8-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 1.0007 1.0017 0.7353 0.99971.0002 0.9998 1.0001 1 1.1927 1.4264 1.7169 2.0738 2.4886 2.8112 u21.0005 1.0004 1.0005 2.2657 2.8429 3.337 3.6717 3.7738 3.5613 3.69053.9984 4.3992 4.8482 5.2041 u3 0.9998 0.9999 1.4855 2.2642 2.842 3.33673.6718 3.775 4.6253 5.4009 6.24 7.1031 7.9262 8.4801 SNR 14 15 16 17 1819 20 21 22 23 24 25 26 27 u1 2.9803 3.0658 3.089 3.0745 3.0551 3.04083.0308 3.0234 3.0183 3.0146 3.0117 3.006 2.9999 3.0181 u2 5.4101 5.50995.4876 5.3868 5.288 5.2157 5.1639 5.1262 5.0982 5.0776 5.0613 5.04675.0116 5.0174 u3 8.7018 8.7025 8.4931 8.1754 7.8925 7.6814 7.5255 7.40937.3204 7.2536 7.2029 7.156 7.1015 7.12 SNR 28 29 30 u1 3.1429 2.58782.6804 u2 5.2147 4.0051 4.2638 u3 7.481 5.6207 5.7796b4) 64-QAM/8-PAM for a Fading Channel (2. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 18 u1 1.0353 1.1062 1.2092 1.34511.5409 1.8112 2.1208 2.3945 2.6067 2.756 2.8505 2.912 2.9496 2.9751 u22.8206 2.9015 3.0799 3.298 3.5826 3.9386 4.3237 4.6577 4.9074 5.07735.1674 5.2201 5.2393 5.2491 u3 3.4534 3.922 4.4154 4.9297 5.5069 6.15946.8108 7.3475 7.7177 7.9488 8.0398 8.068 8.0538 8.0217 SNR 19 20 21 2223 24 25 26 27 28 29 30 u1 2.9907 3.0032 3.0055 3.0126 3.0124 3.01363.0165 3.0156 3.0158 3.016 3.018 3.0183 u2 5.2493 5.2489 5.2365 5.23755.2247 5.2182 5.2165 5.2098 5.207 5.204 5.2036 5.1995 u3 7.9849 7.95287.9035 7.8862 7.8443 7.8194 7.8046 7.7839 7.7661 7.762 7.7569 7.7566c1) 256-QAM or 16-PAM for a Non-Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0097 1.0665 1.0768 1.09301.1066 1.0503 1.0278 1.0000 1.0000 1.0000 1.0000 1.0256 1.1132 u₂ 1.02431.4150 1.2578 1.4817 1.7257 1.9773 2.1334 2.3571 2.6866 2.8218 2.94843.0100 3.0828 u₃ 1.0300 1.6034 1.2587 1.5300 1.7257 1.9773 2.1334 2.36222.7092 2.8892 3.1149 3.2249 3.4673 u₄ 2.6821 3.3596 3.4255 3.7766 3.91384.1612 4.3125 4.4722 4.8316 4.9033 5.1366 5.2497 5.4373 u₅ 2.6821 3.35963.4255 3.7766 3.9375 4.1734 4.4861 4.8450 5.3535 5.5528 5.8510 6.05346.5183 u₆ 3.3063 4.0879 4.3286 4.6970 5.0898 5.6363 6.3912 6.8392 7.60857.9200 8.3122 8.4791 8.8521 u₇ 3.6820 4.7573 4.7284 5.4489 6.2380 6.56757.7493 8.8112 10.0024 10.6021 11.1960 11.3836 11.7747 SNR 18 19 20 21 2223 24 25 26 27 28 29 30 u₁ 1.3440 2.0909 2.7505 2.9606 3.0120 3.01763.0142 3.0104 3.0073 3.0054 3.0042 3.0022 2.9919 u₂ 3.2921 4.0957 4.80955.0402 5.0981 5.0934 5.0719 5.0525 5.0386 5.0269 5.0222 5.0150 5.0017 u₃4.0379 5.5745 6.8101 7.2061 7.2981 7.2676 7.2042 7.1500 7.1120 7.08457.0663 7.0475 7.0199 u₄ 5.9945 7.7068 9.1334 9.6065 9.6891 9.5883 9.44609.3305 9.2485 9.1897 9.1488 9.1103 9.0581 u₅ 7.5727 9.9098 11.748712.3192 12.3427 12.1129 11.8445 11.6314 11.4793 11.3645 11.2861 11.215811.1448 u₆ 9.9517 12.7455 14.9217 15.4925 15.3646 14.9269 14.470414.1111 13.8500 13.6527 13.5110 13.3957 13.2816 u₇ 13.0332 16.395418.9099 19.3657 18.9656 18.2095 17.4738 16.8947 16.4666 16.1368 15.897515.6946 15.5305c2) 256-QAM or 16-PAM for a Fading Channel (1. Option)

SNR 5 6 7 8 9 10 11 12 13 14 15 16 17 u₁ 1.0356 1.0100 1.0290 1.02191.0329 1.0094 1.0111 1.0000 1.0000 1.0001 1.0246 1.1185 1.3950 u₂ 1.38281.3870 1.5299 1.4838 1.7668 1.9127 2.1472 2.2908 2.4733 2.6105 2.70922.8453 3.1765 u₃ 1.3992 1.3870 1.5492 1.4838 1.7668 1.9127 2.1472 2.30512.5255 2.7354 2.9390 3.2706 3.9636 u₄ 3.0045 3.1253 3.3047 3.3824 3.73093.9074 4.1429 4.3242 4.5173 4.6739 4.8281 5.1438 5.9227 u₅ 3.0045 3.14493.3048 3.4113 3.7801 4.0235 4.3590 4.7401 5.0524 5.3659 5.7359 6.31407.4309 u₆ 3.6491 4.1004 4.3581 4.6594 5.1755 5.6876 6.0417 6.6189 7.03047.3939 7.7768 8.4290 9.7743 u₇ 4.3373 4.5258 4.9468 5.3793 5.9000 6.62717.4630 8.7179 9.2916 9.7803 10.2831 11.1015 12.7817 SNR 18 19 20 21 2223 24 25 26 27 28 29 30 u₁ 1.8520 2.2282 2.4888 2.6609 2.7728 2.84312.8888 2.9170 2.9375 2.9504 2.9593 2.9671 2.9692 u₂ 3.7148 4.1544 4.45974.6629 4.7937 4.8730 4.9250 4.9552 4.9771 4.9892 4.9973 5.0074 5.0060 u₃4.9210 5.6758 6.1947 6.5358 6.7533 6.8809 6.9632 7.0090 7.0410 7.05547.0668 7.0806 7.0767 u₄ 7.0428 7.9073 8.4842 8.8475 9.0687 9.1840 9.25159.2802 9.2999 9.2969 9.2999 9.3060 9.2919 u₅ 8.9081 10.0295 10.765811.2198 11.4828 11.6084 11.6720 11.6871 11.6912 11.6733 11.6622 11.661011.6332 u₆ 11.5661 12.8870 13.7176 14.1966 14.4408 14.5284 14.540714.5072 14.4683 14.4127 14.3708 14.3439 14.2915 u₇ 14.9910 16.563717.4984 17.9831 18.1769 18.1849 18.1070 17.9950 17.8844 17.7634 17.670717.6011 17.5056c3) 256-QAM/16-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9987 1 0.8555 0.9986 1.00070.9999 1 1.0001 1.1538 1.2053 1.1098 1.0113 0.9755 0.961 u2 0.99950.9988 0.6438 0.999 1.0022 1.0008 0.9997 1 1.3318 1.4592 1.5806 1.85112.1909 2.5454 u3 1.0006 1.0012 0.7241 0.9997 1.0003 0.9994 1.0002 11.1537 1.2044 1.4081 1.7918 2.1934 2.5919 u4 1.0014 0.9977 0.9802 2.27012.8454 3.336 3.6707 3.7727 4.0051 4.1314 3.8919 3.9933 4.2942 4.6269 u50.9994 0.9966 0.8403 2.261 2.8447 3.3359 3.6718 3.7726 3.5919 3.74493.8725 4.2278 4.6785 5.1556 u6 0.9984 0.9972 1.2098 2.2574 2.8455 3.33813.6727 3.7737 4.0063 4.1297 4.7175 5.7442 6.5854 7.3386 u7 1.0001 0.99961.4732 2.265 2.8465 3.3369 3.6713 3.7738 5.9093 6.4423 6.812 7.64288.6591 9.7477 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 0.96530.9856 1.0251 1.1128 1.3449 2.0965 2.7527 2.9608 3.012 3.0177 3.01433.0103 3.0079 3.0062 u2 2.7901 2.9261 3.0106 3.0821 3.2917 4.1039 4.8115.0404 5.0984 5.0934 5.0717 5.0526 5.0399 5.0306 u3 2.88 3.0661 3.22523.4662 4.0382 5.5877 6.8118 7.2066 7.2996 7.2675 7.2034 7.15 7.11347.0869 u4 4.8939 5.0926 5.2509 5.436 5.9941 7.7231 9.1364 9.6073 9.69079.5882 9.4452 9.3304 9.2506 9.1924 u5 5.5283 5.7961 6.055 6.5161 7.57369.9317 11.7532 12.3202 12.3438 12.1129 11.8432 11.6313 11.4811 11.3712u6 7.8908 8.2396 8.4806 8.8492 9.9513 12.7737 14.9274 15.4938 15.364814.9271 14.4683 14.1107 13.8529 13.661 u7 10.5917 11.0972 11.385311.7713 13.0322 16.4337 18.9135 19.3674 18.9636 18.2094 17.4708 16.894216.4697 16.1476 SNR 28 29 30 u1 3.0044 3.0038 3.003 u2 5.023 5.01785.0128 u3 7.067 7.0512 7.0407 u4 9.1486 9.1126 9.0893 u5 11.2883 11.221711.1749 u6 13.5157 13.3981 13.3164 u7 15.9014 15.7029 15.5677c4) 256-QAM/16-PAM for the Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9798 0.9967 0.9947 0.99711.0007 1.03 1.0688 1.0762 1.0537 1.0342 1.0147 0.9992 0.9918 0.9922 u20.8908 1.0016 0.9934 1.0006 0.9987 1.0588 1.1381 1.2317 1.3585 1.52251.7405 2.0063 2.2615 2.4654 u3 0.9072 1.0041 0.9993 1.0003 0.9997 1.02951.0664 1.1441 1.2863 1.4689 1.7111 2.0037 2.2873 2.5275 u4 1.4244 2.05392.4036 2.6739 2.9049 3.019 3.2106 3.239 3.2891 3.4602 3.7019 3.99664.2761 4.5013 u5 1.3906 2.0371 2.3593 2.6731 2.9097 2.6841 2.8603 3.06273.3005 3.5807 3.9182 4.3056 4.6871 5.0312 u6 1.5899 2.024 2.3535 2.67622.8921 3.0205 3.2171 3.6521 4.2742 4.8242 5.3945 5.997 6.5483 7.0034 u71.6351 2.042 2.3973 2.6721 2.8859 3.9489 4.5222 5.0297 5.6081 6.2717.0282 7.8489 8.6107 9.2424 SNR 14 15 16 17 18 19 20 21 22 23 24 25 2627 u1 0.9989 1.0259 1.1155 1.3963 1.8534 2.2282 2.4891 2.6619 2.77292.8437 2.889 2.9176 2.9379 2.9516 u2 2.6086 2.7135 2.8419 3.1795 3.71754.1541 4.4608 4.664 4.7936 4.8758 4.9257 4.956 4.9778 4.9933 u3 2.73072.9443 3.2659 3.9675 4.9244 5.676 6.197 6.5386 6.7531 6.8857 6.96397.0096 7.0412 7.064 u4 4.6692 4.8339 5.1383 5.9281 7.0475 7.9072 8.48628.8521 9.0685 9.1906 9.253 9.282 9.3008 9.3117 u5 5.3576 5.7413 6.30827.4353 8.9135 10.0292 10.7694 11.2248 11.4823 11.6157 11.6732 11.688111.6943 11.6904 u6 7.3828 7.7887 8.4196 9.7825 11.5726 12.8864 13.721714.2018 14.4402 14.5326 14.5421 14.508 14.472 14.4315 u7 9.7612 10.293811.0879 12.7927 15.0009 16.5632 17.5017 17.9894 18.1764 18.1926 18.117217.9984 17.8904 17.7896 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u12.9597 2.9661 2.9708 2.9726 2.9757 2.979 2.9795 2.9803 2.981 2.9822.9813 2.9795 2.9788 u2 4.9991 5.0047 5.0081 5.009 5.0124 5.0173 5.01455.016 5.0165 5.0165 5.0154 5.0085 5.0096 u3 7.0698 7.0758 7.0795 7.07957.0819 7.0887 7.0822 7.086 7.086 7.0867 7.0883 7.0759 7.0772 u4 9.30299.2996 9.2958 9.2878 9.2861 9.2921 9.2787 9.2803 9.2787 9.2784 9.27859.2623 9.2664 u5 11.668 11.6526 11.6385 11.6222 11.6137 11.6142 11.596911.5934 11.5903 11.5892 11.5893 11.5636 11.561 u6 14.3754 14.333314.2955 14.2621 14.2394 14.2301 14.2009 14.1909 14.1835 14.1804 14.17314.1335 14.1421 u7 17.6749 17.5886 17.5132 17.4498 17.4048 17.374917.3292 17.307 17.2908 17.2734 17.2633 17.208 17.2206d1) 1024-QAM or 32-PAM for a Non-Fading Channel (1. Option)

SNR 8 9 10 11 12 13 14 15 16 17 18 u₁ 1.0067 1.0148 1.0507 1.0476 1.01981.0464 1.0909 1.0037 1.0187 1.0148 1.0251 u₂ 1.0380 1.0523 1.0845 1.08351.0373 1.0701 1.0910 1.0428 1.0711 1.1108 1.2863 u₃ 1.0695 1.0949 1.10461.1376 1.0754 1.0813 1.1644 1.0447 1.0807 1.1364 1.2891 u₄ 1.6402 1.83472.0518 2.5314 2.6729 2.9275 3.0920 2.9924 3.0361 3.0693 3.3256 u₅ 1.67411.9096 2.1058 2.5742 2.7200 2.9512 3.1966 3.0105 3.0631 3.0902 3.3296 u₆1.6802 1.9096 2.1287 2.5742 2.7278 3.0476 3.2399 3.1832 3.3080 3.44183.9436 u₇ 1.7120 1.9314 2.1552 2.6395 2.7641 3.0980 3.3711 3.1850 3.31333.4430 3.9450 u₈ 3.7616 3.9751 4.2512 4.6900 4.7720 5.0430 5.3006 5.16665.2248 5.3743 5.9219 u₉ 3.7988 4.0277 4.3122 4.7622 4.8209 5.1017 5.41565.1666 5.2248 5.3743 5.9219 u₁₀ 3.7988 4.0671 4.3749 4.8789 5.01445.5053 5.8716 5.8269 5.9842 6.2741 7.2272 u₁₁ 3.8518 4.1230 4.39054.8870 5.0144 5.5054 5.8716 5.8763 6.0961 6.4804 7.4547 u₁₂ 4.87325.3269 6.0182 6.8091 7.0796 7.6797 8.0443 7.9004 7.9850 8.3476 9.4109u₁₃ 4.9607 5.3481 6.0182 6.8466 7.0905 7.6878 8.1462 8.2883 8.38568.9683 10.1262 u₁₄ 5.5363 5.9883 6.7380 7.6823 8.1294 8.8170 9.36909.9247 10.1499 11.0046 12.4646 u₁₅ 5.7097 6.5205 7.2058 8.0785 8.43039.8312 10.9109 11.9003 12.0120 13.4835 15.2549 SNR 19 20 21 22 23 24 2526 27 28 29 u₁ 1.0024 1.0006 1.0016 1.0005 1.0031 1.0346 1.2687 2.56882.9137 2.9903 3.0038 u₂ 1.7107 2.5479 2.8831 2.9838 3.0077 3.0243 3.21744.5722 4.9309 5.0103 5.0225 u₃ 1.7141 2.5515 2.8832 2.9845 3.0245 3.11353.6704 6.2334 6.8977 7.0454 7.0642 u₄ 3.6770 4.5909 4.9553 5.0538 5.06155.0609 5.4996 8.2567 8.9703 9.1297 9.1403 u₅ 3.6786 4.5909 4.9553 5.07045.1383 5.3184 6.3316 10.0819 11.0442 11.2591 11.2602 u₆ 4.8209 6.42387.0286 7.1835 7.1646 7.1593 8.0505 12.1692 13.2274 13.4612 13.4368 u₇4.8209 6.4274 7.0642 7.2914 7.4407 7.8023 9.3361 14.2128 15.4757 15.744115.6806 u₈ 6.8262 8.6260 9.3012 9.4393 9.3945 9.5457 11.0297 16.452317.8558 18.1316 18.0048 u₉ 6.8553 8.7222 9.5195 9.8531 10.1506 10.773112.6757 18.7884 20.3719 20.6408 20.4242 u₁₀ 8.6131 10.9071 11.748611.9625 12.0642 12.5104 14.5305 21.3353 23.0690 23.2947 22.9559 u₁₁8.9135 11.4255 12.5514 13.0881 13.5886 14.2704 16.5415 24.1089 25.976126.1177 25.6206 u₁₂ 11.0009 13.7880 14.9096 15.3045 15.6473 16.312418.7922 27.1742 29.1347 29.1436 28.4455 u₁₃ 11.9746 15.2957 16.942517.5792 17.9741 18.6433 21.3263 30.5883 32.5987 32.4209 31.4714 u₁₄14.5395 18.2064 19.8795 20.4586 20.7562 21.3536 24.2238 34.4505 36.462036.0306 34.7706 u₁₅ 17.7040 21.9252 23.6632 24.0824 24.1747 24.620227.6622 38.9891 40.9391 40.1627 38.5012 SNR 30 31 32 33 34 35 36 37 3839 40 u₁ 3.0029 3.0028 3.0023 3.0037 3.0010 3.0022 2.9991 3.0009 2.96302.7120 2.4609 u₂ 5.0173 5.0132 5.0104 5.0116 5.0054 5.0074 5.0111 5.00494.9499 4.2412 3.3493 u₃ 7.0495 7.0372 7.0285 7.0273 7.0167 7.0181 7.03287.0073 6.9154 5.8741 4.7174 u₄ 9.1072 9.0800 9.0612 9.0527 9.0358 9.03499.0456 9.0153 8.8955 7.6262 6.4878 u₅ 11.1981 11.1476 11.1119 11.093311.0668 11.0584 11.0454 11.0325 10.8427 8.9624 7.7169 u₆ 13.3309 13.246513.1864 13.1515 13.1108 13.0955 13.0779 13.0621 12.7897 10.8692 8.5130u₇ 15.5146 15.3830 15.2899 15.2330 15.1738 15.1445 15.0931 15.101314.7269 12.0858 9.8751 u₈ 17.7592 17.5659 17.4290 17.3407 17.256617.2099 17.1422 17.1488 16.6081 13.7050 11.5486 u₉ 20.0760 19.804019.6107 19.4829 19.3658 19.2996 19.1878 19.2029 18.5568 15.1881 12.4136u₁₀ 22.4791 22.1087 21.8439 21.6641 21.5065 21.4089 21.2611 21.279220.1847 16.9468 14.2051 u₁₁ 24.9859 24.4938 24.1410 23.8963 23.686323.5530 23.3458 23.3490 21.2990 18.7549 15.1350 u₁₂ 27.6192 26.979326.5155 26.1908 25.9177 25.7334 25.4559 25.4652 24.3404 20.4199 16.3718u₁₃ 30.4127 29.5936 28.9967 28.5657 28.2131 27.9698 27.6069 27.629325.1817 20.6889 18.1707 u₁₄ 33.4269 32.3855 31.6180 31.0614 30.602030.2801 29.8393 29.8551 28.0675 24.2726 18.9363 u₁₅ 36.7956 35.467734.4795 33.7493 33.1451 32.7195 32.0437 32.1466 29.1598 25.0126 20.2944d2) 1024-QAM or 32-PAM for a Fading Channel (1. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 u₁ 1.0003 1.0000 1.0000 1.0011 1.0000 1.00001.0006 1.0000 1.0002 1.0043 1.0108 u₂ 1.0003 1.0049 1.0163 1.0196 1.02081.0308 1.0214 1.0390 1.0252 1.0803 1.1627 u₃ 1.0027 1.0254 1.0360 1.03811.0582 1.0725 1.0400 1.0475 1.0286 1.1088 1.1942 u₄ 1.0164 1.0686 1.13001.2102 1.2704 1.3984 1.4402 1.5327 1.6809 1.9443 2.2594 u₅ 1.0277 1.07041.1395 1.2359 1.2821 1.4126 1.4586 1.5465 1.6972 1.9733 2.3050 u₆ 1.04561.0894 1.1495 1.2553 1.2994 1.4417 1.4951 1.5465 1.7362 2.0279 2.4395 u₇1.0487 1.1132 1.1734 1.2757 1.3364 1.4849 1.5096 1.5503 1.7364 2.05602.4406 u₈ 1.9738 2.1671 2.3628 2.5480 2.7476 3.0647 3.1661 3.3174 3.57673.8954 4.3049 u₉ 2.0526 2.1986 2.4403 2.6234 2.8083 3.1166 3.2014 3.34033.5857 3.9143 4.3315 u₁₀ 2.0663 2.2340 2.4536 2.6234 2.8196 3.14583.2015 3.3860 3.6394 4.0486 4.6119 u₁₁ 2.1022 2.2898 2.5070 2.68362.8698 3.1887 3.2388 3.3919 3.6572 4.0846 4.6119 u₁₂ 2.4454 2.68942.9825 3.2145 3.4803 3.8713 4.0826 4.4221 4.8650 5.3735 6.0449 u₁₃2.5537 2.7750 3.0830 3.2993 3.6342 4.0375 4.1566 4.4677 4.8650 5.37356.1193 u₁₄ 2.7190 2.9743 3.3004 3.5711 3.9845 4.3829 4.6192 4.98325.4362 6.1354 6.8700 u₁₅ 2.8164 3.1340 3.3947 3.7517 4.0778 4.52404.8297 5.2517 5.7299 6.6103 7.5087 SNR 11 12 13 14 15 16 17 18 19 20 21u₁ 1.0206 1.0240 1.0158 1.0030 1.0094 1.0165 1.0109 1.0003 1.0009 1.00431.0003 u₂ 1.0739 1.1088 1.2267 1.0173 1.0577 1.1641 1.3963 1.6842 2.08932.3787 2.5628 u₃ 1.1015 1.1366 1.2493 1.0173 1.0632 1.1895 1.4131 1.68632.0899 2.3793 2.5641 u₄ 2.3031 2.5070 2.7823 2.6207 2.7531 2.9022 3.17983.5239 3.9928 4.3337 4.5385 u₅ 2.3307 2.5226 2.8092 2.6267 2.7580 2.92223.1944 3.5282 3.9930 4.3342 4.5580 u₆ 2.3962 2.6229 3.0150 2.7411 2.98103.3589 3.9199 4.5765 5.3853 5.9529 6.2800 u₇ 2.4238 2.6526 3.0349 2.74702.9811 3.3605 3.9203 4.5765 5.3906 5.9865 6.3991 u₈ 4.3380 4.5737 4.94614.6738 4.8680 5.2293 5.8532 6.6194 7.5215 8.1146 8.4195 u₉ 4.3743 4.61274.9764 4.6738 4.8680 5.2293 5.8532 6.6415 7.6038 8.3211 8.8558 u₁₀4.6129 4.9434 5.4050 5.3030 5.6793 6.3007 7.1684 8.1999 9.3413 10.108310.5973 u₁₁ 4.6129 4.9434 5.4050 5.3190 5.7268 6.4114 7.3330 8.51239.8455 10.8886 11.6792 u₁₂ 6.2332 6.6912 7.1932 7.0781 7.4631 8.12469.1671 10.4955 11.9313 12.9749 13.7196 u₁₃ 6.2378 6.7067 7.2143 7.43167.8792 8.7397 9.9527 11.6664 13.4007 14.6947 15.6090 u₁₄ 7.2044 7.75318.3908 9.0011 9.5503 10.5383 11.9678 13.9641 15.9024 17.3089 18.2685 u₁₅7.8925 8.6732 9.0513 10.9148 11.5100 12.7890 14.4376 16.9300 19.168020.7369 21.7475 SNR 22 23 24 25 26 27 28 29 30 31 32 u₁ 1.0002 1.07531.5871 2.0792 2.3953 2.5979 2.7284 2.8108 2.8638 2.8972 2.9205 u₂ 2.68212.8032 3.3595 3.9137 4.2801 4.5188 4.6763 4.7770 4.8432 4.8844 4.9121 u₃2.6985 2.9606 4.0489 5.0644 5.7316 6.1639 6.4450 6.6243 6.7411 6.81166.8624 u₄ 4.6475 4.8124 5.9653 7.0563 7.7599 8.2091 8.4995 8.6815 8.79918.8675 8.9155 u₅ 4.7447 5.1854 6.8626 8.3577 9.3324 9.9565 10.358810.6098 10.7698 10.8617 10.9265 u₆ 6.4363 6.7835 8.6319 10.2875 11.352912.0290 12.4603 12.7241 12.8892 12.9778 13.0422 u₇ 6.7723 7.5030 9.819611.8295 13.1294 13.9541 14.4760 14.7917 14.9857 15.0876 15.1596 u₈8.6146 9.2375 11.8029 14.0035 15.3949 16.2563 16.7886 17.0983 17.279717.3649 17.4228 u₉ 9.3840 10.3216 13.3049 15.8351 17.4372 18.423319.0262 19.3679 19.5628 19.6463 19.6994 u₁₀ 11.0496 12.0123 15.345918.1385 19.8764 20.9233 21.5442 21.8783 22.0561 22.1145 22.1450 u₁₁12.3712 13.5373 17.2964 20.4157 22.3392 23.4820 24.1409 24.4781 24.645924.6783 24.6849 u₁₂ 14.3775 15.6118 19.8018 23.2294 25.2925 26.477927.1285 27.4264 27.5506 27.5290 27.4931 u₁₃ 16.3759 17.7521 22.437426.2246 28.4576 29.7039 30.3509 30.6108 30.6865 30.6041 30.5122 u₁₄19.0535 20.5285 25.7859 29.9638 32.3556 33.6202 34.2212 34.3969 34.383534.2046 34.0347 u₁₅ 22.5334 24.1205 30.0937 34.7506 37.3202 38.578639.0930 39.1396 38.9925 38.6816 38.3850 SNR 33 34 35 36 37 38 39 40 u₁2.9354 2.9461 2.9539 2.9566 2.9625 2.9679 2.9706 2.9668 u₂ 4.9294 4.94304.9521 4.9535 4.9610 4.9733 4.9711 4.9647 u₃ 6.8891 6.9128 6.9279 6.93276.9441 6.9639 6.9598 6.9537 u₄ 8.9381 8.9612 8.9734 8.9760 8.9857 9.01179.0034 8.9914 u₅ 10.9554 10.9880 11.0022 11.0031 11.0166 11.0516 11.038111.0244 u₆ 13.0641 13.0956 13.1054 13.1036 13.1132 13.1541 13.133913.1153 u₇ 15.1815 15.2131 15.2214 15.2164 15.2267 15.2711 15.247515.2256 u₈ 17.4273 17.4495 17.4469 17.4330 17.4369 17.4818 17.450317.4219 u₉ 19.6952 19.7108 19.6985 19.6773 19.6762 19.7216 19.685519.6521 u₁₀ 22.1170 22.1128 22.0880 22.0535 22.0433 22.0913 22.037821.9943 u₁₁ 24.6327 24.6090 24.5689 24.5179 24.4941 24.5412 24.476224.4209 u₁₂ 27.3953 27.3392 27.2667 27.1957 27.1547 27.1976 27.109527.0355 u₁₃ 30.3630 30.2747 30.1682 30.0651 30.0017 30.0359 29.927929.8362 u₁₄ 33.8099 33.6615 33.5079 33.3683 33.2557 33.2767 33.141433.0224 u₁₅ 38.0516 37.8298 37.6071 37.3990 37.2354 37.2407 37.084536.9002 SNR 42 44 46 48 50 u₁ 2.9738 2.9727 2.9803 2.9747 2.9755 u₂4.9763 4.9704 4.9831 4.9798 4.9849 u₃ 6.9716 6.9620 6.9761 6.9699 6.9855u₄ 9.0140 8.9995 9.0169 9.0005 9.0175 u₅ 11.0516 11.0383 11.0596 11.027711.0471 u₆ 13.1460 13.1331 13.1545 13.0993 13.1231 u₇ 15.2595 15.245115.2638 15.1874 15.2293 u₈ 17.4578 17.4387 17.4605 17.3555 17.4128 u₉19.6900 19.6695 19.6999 19.5662 19.6282 u₁₀ 22.0331 22.0039 22.034621.8900 21.9543 u₁₁ 24.4634 24.4247 24.4522 24.2985 24.3779 u₁₂ 27.071227.0228 27.0504 26.8712 26.9537 u₁₃ 29.8692 29.7967 29.8201 29.612029.6794 u₁₄ 33.0482 32.9359 32.9517 32.7729 32.8541 u₁₅ 36.8842 36.725536.7204 36.5908 36.7169d3) 1024-QAM/32-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9992 0.9991 0.9626 0.99670.9967 0.9988 0.9997 1.0671 1.0969 1.0363 0.962 1.0001 0.9878 0.9942 u20.9957 0.9942 0.8697 0.9895 0.9965 0.9992 0.9989 1.1388 1.2043 1.21071.1702 0.9997 0.9747 0.966 u3 0.9965 0.9943 0.8971 0.99 0.9962 0.99910.9986 1.0674 1.0955 1.1639 1.2161 0.9996 0.9863 0.9719 u4 0.9971 0.99650.6648 0.99 0.9954 0.9994 1.0008 1.1386 1.2048 1.3562 1.4866 1.82642.2272 2.5533 u5 0.996 0.9939 0.6491 0.9905 0.9956 0.9997 1.001 1.21381.3242 1.4129 1.4414 1.848 2.2217 2.5387 u6 0.9992 1.0019 0.6995 0.99740.9977 0.9998 1.0017 1.1384 1.2058 1.2085 1.1751 1.8267 2.223 2.5691 u70.9999 1.0022 0.719 0.9994 0.9993 1.0004 1.0017 1.0667 1.0964 1.1621.2213 1.8066 2.2286 2.581 u8 1.0018 1.0047 0.9796 2.2704 2.8447 3.33393.6691 4.1038 4.3038 4.1189 3.88 3.962 4.3457 4.661 u9 1.0009 1.00430.9448 2.264 2.8416 3.334 3.6696 3.6418 3.8694 4.0902 4.1993 4.10974.4994 4.7046 u10 0.9975 0.9957 0.8525 2.2387 2.8354 3.336 3.672 3.41193.666 3.7746 3.802 4.2647 4.7161 5.1202 u11 0.9986 0.9982 0.8839 2.24052.8378 3.3375 3.6721 3.6428 3.8684 3.7435 3.6203 4.1131 4.5362 5.0343u12 0.9986 0.9963 1.2974 2.2393 2.8414 3.3349 3.6662 4.1042 4.30484.1203 3.8917 6.185 6.9957 7.2365 u13 0.9975 0.996 1.243 2.2388 2.8383.3348 3.6674 3.6422 3.8687 4.0904 4.2129 5.8337 6.7509 7.454 u14 1.0011.0011 1.4137 2.2601 2.844 3.335 3.6673 4.1032 4.3066 5.0379 5.57076.2198 7.2075 8.594 u15 1.0017 1.0022 1.4853 2.2698 2.8465 3.3339 3.66696.1624 6.9359 7.2501 7.4066 8.6211 9.7438 10.859 SNR 14 15 16 17 18 1920 21 22 23 24 25 26 27 u1 1.0007 1.0027 0.9981 0.9933 0.9936 0.999 11.0001 0.9973 1.0036 1.0338 1.2685 2.568 2.9124 u2 0.9694 0.9834 1.00861.0594 1.2188 1.7124 2.5469 2.8781 2.9836 3.0078 3.024 3.2172 4.57094.9289 u3 0.9681 0.9811 1.0101 1.0676 1.2263 1.7139 2.5465 2.8764 2.98373.0244 3.1126 3.6704 6.2313 6.8942 u4 2.7737 2.9007 2.9741 3.0241 3.1593.6872 4.5907 4.9456 5.0494 5.0625 5.0597 5.4996 8.2546 8.9668 u5 2.77142.9125 2.9988 3.0553 3.1727 3.6864 4.5862 4.9442 5.0663 5.138 5.31756.3322 10.0797 11.0396 u6 2.8418 3.0307 3.1789 3.35 3.7479 4.8324 6.4177.0146 7.1785 7.1643 7.1579 8.0513 12.1665 13.2221 u7 2.846 3.02183.1519 3.3116 3.7215 4.8226 6.4211 7.0502 7.2858 7.4383 7.8018 9.336714.2096 15.4697 u8 4.9072 5.0916 5.2328 5.352 5.6798 6.8426 8.61959.2808 9.4323 9.3928 9.5449 11.0304 16.4487 17.8497 u9 4.8825 5.03255.1573 5.2795 5.6568 6.8702 8.7174 9.4992 9.8449 10.1481 10.7709 12.676818.7845 20.3652 u10 5.4415 5.6696 5.8553 6.1215 6.9014 8.6299 10.895711.7222 11.9532 12.0621 12.5094 14.5322 21.3307 23.0612 u11 5.45 5.76676.0273 6.3484 7.1423 8.9474 11.4173 12.5228 13.0769 13.586 14.268416.5436 24.1032 25.9674 u12 7.6047 7.8958 8.1046 8.3161 9.0363 11.023113.7773 14.8757 15.2913 15.6441 16.3101 18.7948 27.1676 29.1243 u138.0146 8.4122 8.6722 8.9298 9.7542 12.0148 15.2835 16.9016 17.563317.972 18.6404 21.3291 30.5806 32.5873 u14 9.6267 10.3424 10.796811.1339 12.0444 14.5782 18.1947 19.8327 20.4394 20.7517 21.3511 24.227134.4413 36.4503 u15 11.9177 12.7867 13.3749 13.7814 14.8151 17.753221.9096 23.606 24.0612 24.1702 24.6165 27.6663 38.9792 40.9267 SNR 28 2930 31 32 33 34 35 36 37 38 39 40 u1 2.9902 3.0016 3.0038 3.002 3.00243.0017 3.0014 3.0014 2.9988 3.0102 3.0035 2.7197 2.0472 u2 5.01 5.02065.0186 5.0131 5.0105 5.0084 5.006 5.0051 5.0006 5.0192 5.0363 4.41392.9841 u3 7.0446 7.0618 7.0515 7.0373 7.0287 7.022 7.0169 7.0134 7.00447.0244 7.0893 6.2809 3.9607 u4 9.1283 9.1368 9.1105 9.0811 9.0608 9.04669.0367 9.0261 9.0134 9.0332 9.1092 7.9322 5.0898 u5 11.257 11.256211.2029 11.1486 11.1121 11.0856 11.0685 11.0475 11.0277 11.0421 11.13179.6412 6.0761 u6 13.4588 13.4329 13.3374 13.2478 13.1867 13.143 13.110613.0776 13.0484 13.061 13.1503 11.2735 7.1638 u7 15.7417 15.6758 15.522415.3852 15.2907 15.2225 15.173 15.1242 15.0767 15.0837 15.1749 13.13268.1645 u8 18.1292 18.0006 17.7684 17.5682 17.4293 17.3297 17.256917.1873 17.1224 17.1191 17.2333 14.826 9.3331 u9 20.6379 20.419 20.086819.8058 19.6109 19.4704 19.3651 19.2702 19.1868 19.1703 19.3081 16.458910.3444 u10 23.2916 22.9487 22.4913 22.1116 21.8445 21.6501 21.506921.3796 21.2695 21.2328 21.3472 18.0904 11.3035 u11 26.1151 25.610524.9996 24.4967 24.1418 23.8821 23.6873 23.5173 23.3768 23.3264 23.426719.7596 12.4831 u12 29.1412 28.4332 27.6343 26.9825 26.5176 26.175125.9187 25.6964 25.5123 25.421 25.4868 21.3998 13.6002 u13 32.417631.4579 30.4306 29.5967 28.997 28.5515 28.2162 27.9277 27.6916 27.554427.5728 23.1872 14.6124 u14 36.0267 34.7541 33.4466 32.3882 31.618931.0443 30.605 30.2317 29.932 29.7649 29.6897 24.9174 15.8244 u1540.1583 38.4818 36.8177 35.4703 34.4789 33.7311 33.1542 32.6692 32.279532.0045 31.9429 26.7754 16.8182d4) 1024-QAM/32-PAM for a Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9877 0.9983 1.0021 0.996 1.00381.0274 1.0458 1.0252 1.0251 1.0106 1.0022 0.9999 0.9993 0.9997 u2 0.95030.9963 0.9924 1.001 0.9979 1.0502 1.1021 1.093 1.0684 1.0421 1.02261.0034 0.9938 0.9916 u3 0.9615 0.9958 0.9968 0.9963 1.0033 1.0263 1.05081.0681 1.0408 1.0311 1.0201 1.0037 0.9938 0.9911 u4 0.8564 0.9951 0.99820.9969 1.0019 1.0506 1.1052 1.2121 1.3282 1.4929 1.7209 1.983 2.23252.4349 u5 0.8494 0.9967 0.994 0.9991 1.0008 1.073 1.1571 1.2411 1.36451.5094 1.7258 1.9826 2.2312 2.4346 u6 0.8807 0.9994 0.9998 0.9959 1.00251.0482 1.1021 1.1634 1.3105 1.4612 1.6899 1.9706 2.2471 2.486 u7 0.89141.0007 0.9995 0.998 0.9995 1.0236 1.0521 1.1359 1.2768 1.4444 1.68511.9712 2.2486 2.4864 u8 1.3814 2.0455 2.4146 2.6684 2.9175 3.2588 3.48593.2744 3.2804 3.4275 3.6722 3.954 4.2289 4.4576 u9 1.3622 2.044 2.42.6704 2.8872 2.8611 3.0858 3.2456 3.3136 3.4906 3.7323 3.9988 4.2554.4646 u10 1.2981 2.0293 2.3562 2.6608 2.8918 2.6571 2.8799 3.08613.3236 3.5804 3.9166 4.2842 4.6461 4.9706 u11 1.3174 2.0299 2.37112.6666 2.9157 2.8566 3.0645 3.0951 3.294 3.5187 3.8461 4.2212 4.60164.9552 u12 1.5422 2.0304 2.3575 2.6702 2.919 3.2583 3.4956 3.7397 4.46474.8383 5.3122 5.8215 6.3089 6.7222 u13 1.5175 2.0313 2.3446 2.66532.8934 2.8625 3.0965 3.6125 4.257 4.7767 5.3692 5.9729 6.5416 7.0327 u141.604 2.0428 2.3901 2.6689 2.8884 3.265 3.5501 4.3656 4.7788 5.44976.2546 7.0898 7.8656 8.5382 u15 1.6294 2.0466 2.4075 2.6719 2.91294.5146 5.143 5.676 6.3035 6.969 7.8139 8.7306 9.6322 10.4411 SNR 14 1516 17 18 19 20 21 22 23 24 25 26 27 u1 1.0006 1.0003 0.9986 0.99940.9989 1.0005 0.9993 1.0023 1.0042 1.0772 1.5857 2.0789 2.3946 2.5983 u20.9966 1.0149 1.0776 1.2742 1.6871 2.0897 2.3726 2.5667 2.6852 2.80113.3587 3.9147 4.2782 4.5193 u3 0.9957 1.0158 1.0779 1.2749 1.6874 2.08882.3722 2.5683 2.7063 2.9634 4.0473 5.0664 5.7293 6.1649 u4 2.5818 2.68482.7905 3.0323 3.5222 3.9945 4.3233 4.5468 4.6563 4.8127 5.9637 7.05797.7572 8.2107 u5 2.5854 2.6903 2.7982 3.0371 3.522 3.9931 4.325 4.56364.7536 5.1864 6.8591 8.3596 9.3297 9.9594 u6 2.6894 2.882 3.1454 3.68134.5789 5.3843 5.9387 6.2876 6.4513 6.7838 8.6281 10.2901 11.3497 12.0321u7 2.6871 2.8747 3.1351 3.6718 4.5753 5.3894 5.9728 6.4073 6.786 7.50299.816 11.834 13.1252 13.9574 u8 4.6338 4.7815 5.0115 5.5854 6.61787.5206 8.0948 8.4282 8.6367 9.238 11.7978 14.0092 15.3897 16.2598 u94.6222 4.7619 4.9912 5.5804 6.6403 7.6013 8.3014 8.8692 9.4056 10.3213.3009 15.8419 17.4299 18.4269 u10 5.2658 5.5779 6.0174 6.8559 8.19699.3371 10.0842 10.6112 11.0768 12.0115 15.3408 18.1472 19.8671 20.9273u11 5.2889 5.6434 6.134 7.0475 8.5126 9.8429 10.8635 11.6946 12.413.5356 17.2901 20.4243 22.3301 23.4863 u12 7.0625 7.3854 7.8549 8.843610.4887 11.9255 12.9446 13.7334 14.4128 15.6099 19.7947 23.2381 25.282526.4823 u13 7.4575 7.8797 8.4919 9.7042 11.6571 13.3962 14.6601 15.627416.4161 17.7524 22.4306 26.2322 28.4484 29.7085 u14 9.1068 9.635 10.34411.727 13.9522 15.8981 17.2695 18.2933 19.0986 20.5256 25.7783 29.97332.3413 33.6247 u15 11.14 11.7874 12.6414 14.2894 16.9161 19.159120.6892 21.7769 22.5894 24.1254 30.084 34.7629 37.3028 38.5854 SNR 28 2930 31 32 33 34 35 36 37 38 39 40 u1 2.7301 2.8111 2.8638 2.8985 2.92042.9359 2.9464 2.9538 2.959 2.9627 2.9646 2.9686 2.9708 u2 4.6776 4.77774.8422 4.8846 4.9112 4.9307 4.9428 4.952 4.9581 4.9636 4.9649 4.96954.9721 u3 6.4472 6.6249 6.7392 6.8128 6.8596 6.8928 6.913 6.9288 6.93986.9487 6.951 6.9583 6.9643 u4 8.5011 8.6817 8.7961 8.8683 8.9124 8.94388.9619 8.9752 8.9849 8.9938 8.9932 9.0001 9.0054 u5 10.3587 10.608110.7659 10.8639 10.9225 10.9642 10.9877 11.0041 11.0164 11.0274 11.026411.0342 11.0416 u6 12.4587 12.7205 12.8844 12.9827 13.0371 13.076113.095 13.1067 13.1177 13.1268 13.1229 13.1289 13.1362 u7 14.474414.7859 14.98 15.0938 15.153 15.1954 15.2147 15.2242 15.2319 15.242115.2363 15.2411 15.2498 u8 16.7868 17.0907 17.2736 17.3718 17.415317.4442 17.4504 17.4501 17.4511 17.4547 17.4418 17.4433 17.4518 u919.0243 19.3589 19.5552 19.6555 19.6923 19.7141 19.7134 19.7042 19.698919.698 19.6791 19.6776 19.6851 u10 21.5442 21.8683 22.0472 22.124222.1375 22.138 22.1179 22.0915 22.0748 22.0635 22.0342 22.0291 22.033u11 24.1421 24.467 24.6335 24.688 24.6782 24.6569 24.6156 24.573924.5418 24.5191 24.4785 24.4679 24.468 u12 27.1288 27.4152 27.533727.5378 27.4826 27.4215 27.3471 27.2736 27.2191 27.1778 27.119 27.099627.0922 u13 30.3512 30.5985 30.6651 30.6154 30.503 30.398 30.283830.1761 30.0938 30.0323 29.9512 29.9185 29.8979 u14 34.2179 34.381834.3579 34.2186 34.0203 33.8444 33.6739 33.5132 33.3876 33.2927 33.181833.1313 33.0899 u15 39.0866 39.1219 38.9603 38.6961 38.3675 38.093837.8319 37.5978 37.4117 37.2731 37.1096 37.0386 36.9652e1) 4096-QAM or 64-PAM for a Non-Fading Channel (1. Option)

SNR 8 9 10 11 12 13 14 15 16 17 18 u₁ 1.0009 1.0095 1.0017 1.0005 1.00261.0357 1.0462 1.0088 1.0294 1.0550 1.0814 u₂ 1.0034 1.0191 1.0071 1.01031.0058 1.0935 1.0747 1.0271 1.0589 1.1067 1.1275 u₃ 1.0085 1.0328 1.01041.0195 1.0178 1.1234 1.1266 1.0514 1.1024 1.1932 1.2000 u₄ 1.0271 1.06851.0379 1.0755 1.1253 1.2903 1.2950 1.3224 1.3806 1.9358 2.5877 u₅ 1.04251.0933 1.0515 1.0862 1.1495 1.3104 1.3388 1.3527 1.4228 1.9850 2.6735 u₆1.0680 1.1256 1.0680 1.0948 1.1750 1.3332 1.3865 1.3620 1.4469 2.05852.7203 u₇ 1.0914 1.1453 1.0851 1.1268 1.1974 1.3824 1.4096 1.3754 1.47022.1306 2.7772 u₈ 1.6408 1.9406 2.1732 2.4538 2.7812 3.2032 3.3168 3.32153.4226 4.0242 4.7576 u₉ 1.6739 1.9863 2.2032 2.4732 2.8165 3.2260 3.36523.3288 3.4528 4.1132 4.8002 u₁₀ 1.7194 2.0417 2.2381 2.5159 2.83423.2727 3.4215 3.3467 3.4850 4.1566 4.8626 u₁₁ 1.7336 2.0649 2.24822.5421 2.8665 3.3094 3.4483 3.3743 3.5120 4.2105 4.9374 u₁₂ 1.73362.0649 2.2482 2.5654 2.9673 3.4823 3.6899 3.7007 3.9353 5.0951 6.3475u₁₃ 1.7489 2.0891 2.2680 2.5736 2.9882 3.5109 3.7310 3.7351 3.97525.1790 6.4107 u₁₄ 1.7667 2.1100 2.2697 2.5749 2.9882 3.5472 3.76533.7530 4.0006 5.2035 6.4781 u₁₅ 1.7858 2.1333 2.2705 2.5880 2.99543.6091 3.7893 3.7599 4.0301 5.3100 6.5484 u₁₆ 3.7227 4.1178 4.31664.6107 4.9833 5.5502 5.7186 5.6573 5.9066 7.1262 8.4751 u₁₇ 3.74184.1491 4.3322 4.6276 4.9903 5.5822 5.7506 5.6655 5.9204 7.2088 8.5684u₁₈ 3.7590 4.1737 4.3574 4.6571 5.0237 5.6385 5.8167 5.6849 5.93707.2417 8.5939 u₁₉ 3.7960 4.2200 4.3712 4.6746 5.0441 5.6775 5.87285.7212 5.9817 7.2914 8.6700 u₂₀ 3.8009 4.2440 4.4357 4.8048 5.26396.0310 6.3672 6.3727 6.8343 8.5615 10.3314 u₂₁ 3.8124 4.2614 4.44614.8333 5.2981 6.0708 6.4211 6.4165 6.8835 8.6242 10.4036 u₂₂ 3.85234.2874 4.4500 4.8427 5.3090 6.0708 6.4211 6.4165 6.9279 8.7014 10.5216u₂₃ 3.8737 4.3357 4.4807 4.8543 5.3363 6.1026 6.4513 6.4233 6.97318.8015 10.5873 u₂₄ 4.8434 5.5231 5.8999 6.5381 7.2235 8.1484 8.50198.3784 8.8105 10.5696 12.5476 u₂₅ 4.9258 5.5864 5.9652 6.5983 7.26848.1872 8.5620 8.4081 8.8693 10.6847 12.6596 u₂₆ 4.9451 5.6415 5.97786.5984 7.2774 8.2065 8.5897 8.4766 9.1103 11.0060 13.0289 u₂₇ 5.03095.7430 6.0828 6.6419 7.3205 8.2309 8.6088 8.4887 9.1104 11.0060 13.0289u₂₈ 5.4098 6.2244 6.6305 7.3617 8.0157 9.2080 9.7789 9.9190 10.749512.8951 15.2014 u₂₉ 5.5000 6.3459 6.7055 7.4383 8.1449 9.3149 9.85189.9298 10.7503 12.8995 15.2179 u₃₀ 5.7152 6.5427 7.0184 7.8330 8.61009.8433 10.6486 10.6096 11.8462 13.9129 16.3707 u₃₁ 5.8780 6.7570 7.28588.0687 8.7350 10.1300 10.9482 10.8858 12.3898 14.9464 17.4057 SNR 19 2021 22 23 24 25 26 27 28 29 u₁ 1.0483 1.0007 1.0044 1.0055 1.0013 1.00091.0008 1.0004 1.0002 1.0009 1.0000 u₂ 1.0613 1.0233 1.0049 1.0067 1.00421.0169 1.1155 2.1473 2.7977 2.9554 2.9938 u₃ 1.0869 1.0300 1.0156 1.01261.0156 1.0172 1.1158 2.1476 2.7982 2.9562 2.9938 u₄ 2.3556 2.7238 2.90642.9831 3.0040 3.0164 3.0800 4.1326 4.8095 4.9735 5.0126 u₅ 2.3688 2.73272.9092 2.9851 3.0143 3.0175 3.0803 4.1329 4.8098 4.9740 5.0127 u₆ 2.40712.7463 2.9108 2.9891 3.0189 3.0684 3.3125 5.4313 6.6706 6.9751 7.0470 u₇2.4309 2.7844 2.9252 2.9939 3.0209 3.0687 3.3127 5.4321 6.6709 6.97557.0476 u₈ 4.4042 4.7555 4.9733 5.0568 5.0728 5.0540 5.1743 7.3914 8.72309.0520 9.1240 u₉ 4.4505 4.7853 4.9821 5.0665 5.0763 5.0545 5.1744 7.39198.7232 9.0521 9.1269 u₁₀ 4.4768 4.8087 4.9864 5.0786 5.1205 5.22475.6985 8.9330 10.7048 11.1492 11.2396 u₁₁ 4.4984 4.8151 4.9894 5.08045.1241 5.2259 5.6990 8.9335 10.7052 11.1499 11.2521 u₁₂ 6.0304 6.67467.0482 7.1894 7.1853 7.1332 7.4320 10.9015 12.8463 13.3324 13.4094 u₁₃6.0394 6.7008 7.0583 7.1926 7.1891 7.1344 7.4326 10.9021 12.8463 13.337213.4549 u₁₄ 6.0730 6.7081 7.0832 7.2853 7.3954 7.6181 8.4317 12.711515.0078 15.5775 15.6226 u₁₅ 6.1073 6.7375 7.0832 7.2884 7.4045 7.61848.4328 12.7116 15.0103 15.6018 15.7683 u₁₆ 8.1524 8.8607 9.3063 9.45159.4026 9.4234 10.0879 14.7765 17.3133 17.9142 17.8813 u₁₇ 8.1720 8.89629.3102 9.4574 9.4108 9.4236 10.0879 14.7780 17.3310 18.0102 18.2795 u₁₈8.2313 8.9543 9.4881 9.7987 10.0367 10.4715 11.5465 16.8714 19.706920.3186 20.2643 u₁₉ 8.2425 8.9679 9.4972 9.8026 10.0398 10.4715 11.551316.8932 19.7984 20.6313 21.1418 u₂₀ 10.1358 11.0877 11.6875 11.943311.9948 12.2390 13.2621 19.1416 22.2235 22.8444 23.0106 u₂₁ 10.208311.1511 11.7122 11.9433 11.9948 12.2473 13.3038 19.2585 22.5518 23.644424.4435 u₂₂ 10.4647 11.5011 12.3809 12.9249 13.3478 13.8662 15.035021.5237 24.8994 25.7504 26.2833 u₂₃ 10.4667 11.5016 12.3809 12.935213.3886 13.9623 15.2365 21.9595 25.7968 27.2622 28.0976 u₂₄ 12.589213.7714 14.6800 15.1061 15.3331 15.7560 16.9792 24.1820 28.0789 29.344430.1001 u₂₅ 12.5892 13.7714 14.6898 15.2127 15.5317 16.1253 17.604925.3100 29.8341 31.4219 32.2373 u₂₆ 13.4094 14.7156 16.2278 17.043417.4121 17.9163 19.3517 27.5432 32.1791 33.7649 34.5644 u₂₇ 13.615815.0373 16.6096 17.6500 18.1533 18.9388 20.7325 29.6202 34.6720 36.339237.0984 u₂₈ 15.7576 17.2752 18.8400 19.7714 20.1992 20.8666 22.640132.1698 37.5238 39.2039 39.8717 u₂₉ 16.4104 18.0503 19.8935 21.373522.0959 22.9213 24.8156 35.1006 40.7639 42.4017 42.9261 u₃₀ 18.568420.5641 22.6573 24.0450 24.6870 25.4664 27.4064 38.5288 44.4858 46.019646.3385 u₃₁ 21.1733 23.6230 26.0750 27.5013 27.9919 28.6401 30.571742.6611 48.9075 50.2608 50.2913 SNR 30 31 32 33 34 35 36 37 38 39 40 u₁1.0001 1.0248 2.4408 2.8945 2.9839 2.9994 3.0018 3.0006 3.0003 3.00012.9997 u₂ 3.0017 3.0182 4.4380 4.8985 4.9886 5.0033 5.0058 5.0032 5.00245.0018 5.0008 u₃ 3.0030 3.0632 5.9156 6.8070 6.9830 7.0115 7.0140 7.00897.0069 7.0048 7.0037 u₄ 5.0173 5.0328 7.9059 8.8226 9.0024 9.0302 9.02889.0193 9.0151 9.0102 9.0071 u₅ 5.0216 5.1327 9.4507 10.7591 11.019511.0577 11.0516 11.0358 11.0282 11.0193 11.0115 u₆ 7.0498 7.0422 11.435712.7957 13.0656 13.0993 13.0845 13.0595 13.0468 13.0326 13.0195 u₇7.0641 7.2652 13.0665 14.7736 15.1170 15.1551 15.1295 15.0921 15.072115.0515 15.0306 u₈ 9.1060 9.0644 15.0535 16.8418 17.2002 17.2304 17.188417.1352 17.1049 17.0757 17.0463 u₉ 9.1497 9.5244 16.7818 18.8755 19.299819.3267 19.2631 19.1895 19.1460 19.1067 19.0675 u₁₀ 11.1813 11.185018.7842 20.9896 21.4336 21.4475 21.3554 21.2573 21.1971 21.1455 21.0958u₁₁ 11.3033 11.9919 20.6171 23.0931 23.5947 23.5943 23.4675 23.340023.2595 23.1929 23.1300 u₁₂ 13.2745 13.5314 22.6537 25.2693 25.795725.7708 25.6021 25.4389 25.3346 25.2505 25.1715 u₁₃ 13.5814 14.656024.5978 27.4601 28.0325 27.9792 27.7614 27.5562 27.4240 27.3180 27.2219u₁₄ 15.4281 16.1335 26.6926 29.7208 30.3180 30.2241 29.9475 29.693729.5290 29.3975 29.2822 u₁₅ 16.0896 17.4553 28.7584 32.0195 32.649732.5080 32.1630 31.8534 31.6506 31.4900 31.3522 u₁₆ 17.8031 18.945930.9410 34.3908 35.0362 34.8341 34.4104 34.0374 33.7912 33.5976 33.4333u₁₇ 18.9158 20.3994 33.1475 36.8221 37.4807 37.2058 36.6926 36.247835.9521 35.7214 35.5286 u₁₈ 20.5417 21.9560 35.4574 39.3347 39.990739.6274 39.0134 38.4877 38.1359 37.8626 37.6368 u₁₉ 21.9857 23.535137.8330 41.9281 42.5704 42.1029 41.3762 40.7588 40.3444 40.0228 39.7614u₂₀ 23.6361 25.2008 40.3158 44.6167 45.2248 44.6370 43.7840 43.065742.5801 42.2047 41.9019 u₂₁ 25.2935 26.9290 42.9015 47.4057 47.961347.2349 46.2412 45.4110 44.8462 44.4090 44.0606 u₂₂ 27.0746 28.750445.6132 50.3061 50.7879 49.9025 48.7528 47.7990 47.1463 46.6413 46.2405u₂₃ 28.9429 30.6660 48.4574 53.3265 53.7113 52.6466 51.3243 50.234449.4838 48.9030 48.4433 u₂₄ 30.9398 32.6931 51.4505 56.4788 56.740855.4760 53.9630 52.7229 51.8619 51.1973 50.6724 u₂₅ 33.0715 34.841254.6068 59.7763 59.8883 58.4008 56.6777 55.2711 54.2893 53.5305 52.9293u₂₆ 35.3606 37.1247 57.9431 63.2360 63.1703 61.4335 59.4783 57.889956.7734 55.9080 55.2244 u₂₇ 37.8240 39.5605 61.4829 66.8796 66.607364.5910 62.3797 60.5886 59.3222 58.3376 57.5609 u₂₈ 40.4876 42.171965.2585 70.7389 70.2237 67.8970 65.4018 63.3861 61.9504 60.8316 59.9460u₂₉ 43.3896 44.9941 69.3198 74.8651 74.0651 71.3880 68.5763 66.307264.6797 63.4096 62.3996 u₃₀ 46.6014 48.0918 73.7587 79.3419 78.208375.1280 71.9563 69.3942 67.5467 66.1014 64.9470 u₃₁ 50.2840 51.616678.7813 84.3684 82.8265 79.2656 75.6675 72.7558 70.6393 68.9832 67.6450e2) 4096-QAM or 64-PAM for a Fading Channel (1. Option)

SNR 10 12 14 16 18 20 22 24 26 28 30 u₁ 1.0037 1.0034 1.0348 1.09521.0016 1.0009 1.0005 1.0084 1.0011 1.0013 1.4601 u₂ 1.0162 1.0343 1.06171.1176 1.0241 1.0018 1.0036 1.4936 2.2772 2.6447 3.2217 u₃ 1.0240 1.06781.0884 1.1793 1.0305 1.0041 1.0043 1.4944 2.2777 2.6458 3.6969 u₄ 1.19211.3907 1.5640 2.0417 2.0126 2.3581 2.6689 3.2663 4.1425 4.5751 5.6208 u₅1.2171 1.4100 1.5873 2.1063 2.0228 2.3589 2.6691 3.2663 4.1430 4.57626.1651 u₆ 1.2361 1.4531 1.6033 2.1127 2.0502 2.3605 2.6803 3.8388 5.47716.2622 7.8852 u₇ 1.2492 1.4877 1.6363 2.1955 2.0517 2.3634 2.6818 3.85525.4782 6.2644 8.5434 u₈ 2.3653 2.8845 3.2972 3.9998 3.8921 4.3057 4.64635.7758 7.4940 8.3068 10.4374 u₉ 2.3776 2.9044 3.3210 4.0789 3.90274.3085 4.6470 5.7801 7.4956 8.3148 11.2098 u₁₀ 2.4146 2.9464 3.34314.0949 3.9258 4.3091 4.7142 6.5005 8.9584 10.0754 12.8922 u₁₁ 2.43302.9727 3.3727 4.1576 3.9303 4.3106 4.7159 6.5026 8.9599 10.1075 13.7819u₁₂ 2.5921 3.2909 3.8752 5.0460 5.1105 5.9019 6.4314 8.2437 10.941612.1137 15.6075 u₁₃ 2.6018 3.3308 3.8838 5.1032 5.1251 5.9026 6.43228.2470 10.9430 12.2240 16.6372 u₁₄ 2.6036 3.3538 3.9079 5.1106 5.15775.9275 6.6966 9.2839 12.6130 13.9827 18.3518 u₁₅ 2.6134 3.3538 3.95755.2402 5.1622 5.9305 6.6977 9.2923 12.6172 14.2759 19.5480 u₁₆ 4.47245.2413 5.8593 7.1349 7.1838 8.0530 8.5878 11.2148 14.8247 16.191021.4467 u₁₇ 4.4904 5.2557 5.9016 7.2435 7.2025 8.0584 8.5900 11.222414.8505 16.7578 22.7923 u₁₈ 4.5233 5.2967 5.9330 7.2709 7.2402 8.22449.2676 12.5840 16.7154 18.3893 24.6241 u₁₉ 4.5370 5.3428 5.9400 7.31567.2402 8.2272 9.2676 12.5847 16.8401 19.2507 26.1464 u₂₀ 4.7553 5.77666.6383 8.4305 8.7991 10.0062 10.9491 14.5161 18.9533 21.0189 28.1725 u₂₁4.7821 5.8104 6.6641 8.4825 8.8222 10.0149 10.9503 14.5520 19.367422.1700 29.8997 u₂₂ 4.8082 5.8291 6.6807 8.5209 9.0392 10.6920 12.186516.2361 21.2176 23.9044 32.0068 u₂₃ 4.8130 5.8737 6.7033 8.6186 9.042210.6920 12.2150 16.4697 22.1503 25.3694 34.0023 u₂₄ 6.2441 7.4671 8.530310.4806 10.9914 12.7390 14.0922 18.4450 24.2033 27.3692 36.4075 u₂₅6.2893 7.4955 8.5634 10.5693 10.9914 12.7601 14.2864 19.1390 25.638829.1536 38.7203 u₂₆ 6.2893 7.5445 8.6516 10.7902 11.8153 14.1858 15.847220.9184 27.7224 31.3403 41.3928 u₂₇ 6.3436 7.6168 8.6551 10.7902 11.893914.5324 16.6065 22.3106 29.7261 33.5729 44.1720 u₂₈ 7.0226 8.5293 9.924412.4877 13.6889 16.4941 18.4985 24.4836 32.3433 36.2788 47.4221 u₂₉7.0606 8.5418 9.9244 12.4922 14.1769 17.7125 20.1454 26.6758 35.130739.2095 50.9584 u₃₀ 7.4057 9.0421 10.6101 13.4485 15.9473 20.049222.5947 29.6354 38.6833 42.8367 55.2496 u₃₁ 7.6853 9.2770 10.970013.9607 18.0971 23.1093 25.8301 33.4923 43.2861 47.4796 60.6968 SNR 3234 36 38 40 42 44 u₁ 2.3630 2.7143 2.8569 2.9146 2.9430 2.9572 2.9626 u₂4.2240 4.6431 4.8201 4.8928 4.9295 4.9485 4.9531 u₃ 5.5916 6.3624 6.68256.8138 6.8769 6.9108 6.9193 u₄ 7.5711 8.3609 8.6875 8.8217 8.8852 8.91958.9261 u₅ 8.9677 10.1017 10.5677 10.7565 10.8452 10.8923 10.9017 u₆10.8558 12.0656 12.5624 12.7646 12.8566 12.9054 12.9128 u₇ 12.310013.8453 14.4705 14.7240 14.8372 14.8969 14.9042 u₈ 14.3495 15.907916.5327 16.7803 16.8878 16.9453 16.9457 u₉ 15.8626 17.7314 18.476418.7717 18.8959 18.9623 18.9619 u₁₀ 17.8122 19.7689 20.5381 20.841020.9630 21.0277 21.0190 u₁₁ 19.4002 21.6494 22.5319 22.8716 23.005123.0767 23.0663 u₁₂ 21.4914 23.7930 24.6692 25.0032 25.1259 25.189025.1683 u₁₃ 23.1749 25.7482 26.7175 27.0846 27.2145 27.2800 27.2540 u₁₄25.2444 27.9133 28.8962 29.2543 29.3711 29.4289 29.3923 u₁₅ 27.055429.9674 31.0256 31.4026 31.5200 31.5729 31.5300 u₁₆ 29.3071 32.278133.3164 33.6672 33.7575 33.7939 33.7339 u₁₇ 31.2488 34.4427 35.537235.8963 35.9772 36.0047 35.9322 u₁₈ 33.5157 36.8096 37.8974 38.227938.2797 38.2878 38.1965 u₁₉ 35.6233 39.1139 40.2361 40.5572 40.589440.5810 40.4746 u₂₀ 38.1010 41.6634 42.7477 43.0181 43.0067 42.968142.8356 u₂₁ 40.4118 44.1431 45.2395 45.4777 45.4325 45.3693 45.2134 u₂₂43.0288 46.8438 47.9000 48.0709 47.9708 47.8722 47.6880 u₂₃ 45.611649.5583 50.5912 50.7048 50.5545 50.4196 50.2024 u₂₄ 48.5564 52.552353.4949 53.5164 53.2904 53.1044 52.8455 u₂₅ 51.4802 55.5697 56.453256.3844 56.0878 55.8498 55.5491 u₂₆ 54.7552 58.8833 59.6566 59.461259.0692 58.7671 58.4167 u₂₇ 58.1823 62.3637 63.0156 62.6864 62.189661.8161 61.4120 u₂₈ 62.1034 66.2736 66.7414 66.2379 65.6055 65.135264.6642 u₂₉ 66.3748 70.5252 70.7893 70.0851 69.2959 68.7220 68.1765 u₃₀71.4868 75.5508 75.5368 74.5533 73.5731 72.8440 72.1957 u₃₁ 77.920781.8329 81.4363 80.0774 78.8139 77.8906 77.1759e3) 4096-QAM/64-PAM for a Non-Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9997 0.9978 0.9991 1 1.00071.0007 1 0.9557 1.0614 0.9551 0.98 0.9906 0.9983 1.0028 u2 0.9987 0.99640.9907 0.9992 1.0007 1.0013 0.9998 0.9995 1.132 1.0662 0.9665 0.99290.9872 0.9951 u3 0.9992 0.9959 0.9909 1.0013 1.0018 1.0022 0.9998 1.04551.0635 1.1175 0.9872 1.0026 0.9889 0.9923 u4 0.9952 0.9939 0.9506 0.99120.9956 0.9997 0.9991 1.0963 1.1367 1.2469 1.0968 1.0043 0.9773 0.9706 u50.9949 0.9927 0.9497 0.9904 0.9958 1.0001 0.999 1.0477 1.2106 1.19141.0729 0.9947 0.9757 0.9733 u6 0.9959 0.9925 0.9569 0.9928 0.9977 1.00070.999 1.0005 1.1354 1.0632 1.0886 0.9926 0.9867 0.9808 u7 0.9964 0.99250.9572 0.9948 0.9985 1.0012 0.9989 1.0469 1.067 1.1141 1.1127 1.00220.9885 0.9781 u8 0.9979 0.996 0.82 0.9969 1.0009 1.0011 0.9982 1.09531.1392 1.2422 1.5245 1.8225 2.2129 2.5779 u9 0.9971 0.9926 0.8212 0.99460.9999 1.0006 0.9981 1.0475 1.2127 1.1856 1.4974 1.8028 2.201 2.5773 u100.9956 0.9897 0.8169 0.9928 0.9977 1.0004 0.998 1.0967 1.2926 1.32881.484 1.8262 2.1995 2.564 u11 0.9956 0.988 0.8184 0.992 0.9969 0.99970.9977 1.1472 1.2149 1.3855 1.5124 1.8468 2.2116 2.5645 u12 0.99991.0001 0.8477 1.0019 1.0015 1 0.998 1.0951 1.1374 1.2436 1.3501 1.82282.2139 2.5865 u13 0.9993 0.9984 0.8477 1.0004 1.0011 0.9998 0.9979 1.0471.2107 1.1876 1.3224 1.8029 2.2021 2.5859 u14 1.0002 0.9981 0.85391.0011 1.0023 0.9996 0.9977 1.0003 1.1352 1.059 1.338 1.781 2.20322.5981 u15 1.0006 0.9988 0.8548 1.0027 1.0023 0.9993 0.9976 1.04661.0674 1.1096 1.365 1.7998 2.2143 2.599 u16 1.0013 0.9984 1.3062 2.28082.8695 3.3381 3.672 3.6931 4.5055 4.0594 3.6916 3.9511 4.3515 4.733 u171.0009 0.9976 1.306 2.276 2.8682 3.3383 3.6706 4.1143 4.0708 4.49 3.79523.9685 4.3262 4.6905 u18 1.0001 0.9975 1.2944 2.2716 2.8549 3.3373 3.6683.692 3.8547 3.9737 3.9649 4.1043 4.4877 4.7651 u19 1.0006 0.9989 1.29622.2767 2.8579 3.3377 3.6688 3.4797 4.0617 3.7447 3.8381 4.0787 4.51024.8115 u20 0.9966 0.9843 1.2316 2.2476 2.8174 3.3366 3.6668 3.33883.8426 3.5963 3.7694 4.2066 4.6844 5.1505 u21 0.9965 0.9862 1.23162.2428 2.816 3.3366 3.6654 3.4788 3.7127 3.7506 3.8549 4.2413 4.66955.1004 u22 0.9979 0.9883 1.2438 2.2472 2.8316 3.338 3.6687 3.693 3.85043.9858 3.7378 4.1047 4.4864 4.988 u23 0.9988 0.9908 1.2452 2.2521 2.83443.3383 3.6697 3.4793 4.0539 3.7531 3.6629 4.0789 4.5089 5.0366 u240.9975 0.9885 1.5288 2.2442 2.8217 3.3383 3.6695 3.695 4.5123 4.04594.3425 6.0223 6.8569 7.2668 u25 0.9969 0.9892 1.527 2.2404 2.8202 3.33773.6672 4.1199 4.0697 4.4707 4.5777 6.3293 7.2964 7.5851 u26 0.99570.9906 1.5113 2.237 2.8068 3.3353 3.6622 3.6994 3.8542 3.9657 4.70925.9321 6.867 7.6187 u27 0.996 0.992 1.5119 2.2422 2.8098 3.3356 3.6633.4819 4.0606 3.7388 4.5292 5.7308 6.6111 7.3641 u28 1.0002 0.99311.6026 2.2672 2.849 3.34 3.6708 3.6937 4.5158 4.0294 5.7423 6.024 6.84858.1001 u29 0.9996 0.9947 1.6004 2.264 2.8464 3.3382 3.6682 4.1221 4.07424.4504 5.71 6.3295 7.2893 8.6424 u30 1.0003 0.9972 1.6155 2.2689 2.863.3379 3.6703 6.9367 4.5402 6.1369 6.5297 7.621 8.7159 9.8487 u31 1.00051.0011 1.6156 2.2746 2.8614 3.3359 3.6701 4.1219 7.7332 7.8583 8.28359.5686 10.848 12.0736 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u11.0012 1.0004 1.0001 1.0001 1.0017 0.9994 0.9991 1.0002 1.0004 0.99881.0002 1.0002 0.9995 0.9998 u2 1.0012 1.0025 0.9995 0.9931 0.9949 0.99780.9973 0.9989 0.9993 0.9997 1.0165 1.1141 2.1397 2.7888 u3 1.0002 1.00270.9992 0.9935 0.9925 0.9974 0.9973 1 0.9997 1.0012 1.0173 1.1147 2.14052.7905 u4 0.9684 0.9816 1.0059 1.0493 1.182 1.5796 2.455 2.8426 2.97143.0025 3.0148 3.08 4.1242 4.7995 u5 0.9695 0.9821 1.006 1.0522 1.18241.5808 2.4551 2.8429 2.9714 3.0028 3.0143 3.0802 4.124 4.8013 u6 0.96970.9806 1.0066 1.0576 1.1891 1.5819 2.4541 2.8411 2.9706 3.0134 3.06633.3089 5.4109 6.6532 u7 0.9688 0.9802 1.0065 1.0566 1.188 1.5815 2.45432.8404 2.9705 3.0122 3.0667 3.3087 5.4124 6.6551 u8 2.7742 2.898 2.97073.0198 3.1266 3.5406 4.4866 4.9057 5.0421 5.061 5.0494 5.1723 7.36928.7048 u9 2.7759 2.8996 2.9696 3.016 3.1241 3.5415 4.4867 4.9067 5.04325.0601 5.0501 5.1727 7.3707 8.706 u10 2.7715 2.9072 2.9916 3.0457 3.14023.541 4.4834 4.9035 5.0525 5.1122 5.2228 5.6928 8.9013 10.681 u11 2.772.9062 2.9926 3.0494 3.1422 3.5425 4.4833 4.9039 5.0525 5.1118 5.22175.6928 8.9024 10.6801 u12 2.8379 3.0216 3.1657 3.3215 3.6581 4.55496.2418 6.9491 7.1699 7.1725 7.1285 7.4272 10.8677 12.8191 u13 2.83933.0233 3.1642 3.3159 3.6531 4.5542 6.2414 6.9493 7.1687 7.1707 7.12927.4281 10.8681 12.8187 u14 2.844 3.017 3.1421 3.2814 3.6249 4.54456.2417 6.9759 7.25 7.3803 7.6122 8.4242 12.6721 14.9756 u15 2.843 3.01583.1438 3.2861 3.6295 4.5453 6.2415 6.9762 7.2509 7.3814 7.6109 8.424112.6723 14.9747 u16 4.911 5.0847 5.2173 5.3247 5.5906 6.5342 8.42529.2104 9.4291 9.3921 9.4171 10.0811 14.7326 17.2923 u17 4.8946 5.0785.2225 5.3361 5.5964 6.5309 8.4176 9.2059 9.4328 9.3936 9.4161 10.079914.7331 17.2755 u18 4.8828 5.032 5.1525 5.263 5.5632 6.5493 8.49399.3909 9.7733 10.0241 10.4656 11.538 16.821 19.7523 u19 4.8993 5.03895.1478 5.2534 5.5595 6.5509 8.5005 9.3955 9.768 10.0192 10.4628 11.540616.8423 19.666 u20 5.4537 5.6751 5.8353 6.0525 6.7077 8.1966 10.633911.6235 11.9277 11.9919 12.2335 13.2526 19.0855 22.4952 u21 5.4274 5.6615.8447 6.0828 6.7436 8.2344 10.6663 11.6306 11.9181 11.9835 12.240613.2955 19.2025 22.1794 u22 5.4211 5.7314 5.9947 6.2932 6.9708 8.515411.1197 12.3574 12.9096 13.3504 13.8605 15.0255 21.46 25.7242 u23 5.4465.7457 5.9865 6.2653 6.934 8.4705 11.0711 12.3354 12.9262 13.398513.9572 15.2319 21.8968 24.8484 u24 7.601 7.9092 8.1116 8.2986 8.884310.5567 13.4789 14.6975 15.1159 15.345 15.7488 16.9733 24.1121 29.7447u25 7.6905 7.9139 8.0671 8.234 8.8098 10.4713 13.4082 14.7119 15.228715.5598 16.121 17.6005 25.2362 28.0103 u26 8.0227 8.3661 8.5885 8.79129.4292 11.2659 14.6004 16.3761 17.081 17.4332 17.9118 19.3511 27.465834.5679 u27 7.8908 8.3208 8.642 8.9175 9.6219 11.5386 14.97 16.835817.7127 18.2141 18.9411 20.7343 29.5377 32.086 u28 9.4399 10.049610.4616 10.7875 11.5373 13.6107 17.3205 19.1194 19.8684 20.2666 20.868822.6464 32.0788 40.6327 u29 9.7624 10.4834 10.962 11.3065 12.090914.2876 18.2519 20.3764 21.561 22.2111 22.9314 24.8269 35.0018 37.4081u30 10.8696 11.8503 12.6479 13.2236 14.1807 16.6639 21.0844 23.237224.2835 24.8299 25.4818 27.4224 38.4187 45.0872 u31 13.0935 14.085114.9452 15.6218 16.7225 19.5472 24.5629 26.8501 27.8003 28.1675 28.656830.5887 42.5428 49.499 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u10.9976 0.9987 1.0014 1.025 2.4413 2.8939 2.9843 2.9997 3.0019 3.00073.0007 3.0003 2.9995 u2 2.9488 2.9915 3.0025 3.018 4.4383 4.8976 4.98955.0043 5.0061 5.0036 5.003 5.0018 5.001 u3 2.9479 2.9924 3.0037 3.06325.9167 6.8058 6.9842 7.0135 7.0137 7.0097 7.0074 7.0054 7.0045 u4 4.96195.0094 5.0187 5.0331 7.9068 8.8211 9.0048 9.0324 9.0288 9.0203 9.01529.0116 9.0111 u5 4.9639 5.011 5.0222 5.1327 9.4519 10.7571 11.022411.0604 11.0525 11.0369 11.0279 11.0206 11.0185 u6 6.9622 7.042 7.05217.0424 11.4366 12.7933 13.0677 13.1031 13.086 13.0608 13.0457 13.034113.0292 u7 6.9646 7.0451 7.0661 7.2657 13.0678 14.7709 15.1192 15.160415.1306 15.0937 15.0694 15.0521 15.0437 u8 9.0372 9.1166 9.1087 9.064515.0544 16.8389 17.2032 17.2373 17.1893 17.1369 17.1017 17.0762 17.0621u9 9.0366 9.12 9.1529 9.5267 16.783 18.8721 19.3026 19.3344 19.264319.1918 19.1426 19.1063 19.0849 u10 11.1331 11.2301 11.1846 11.186818.7849 20.9854 21.4382 21.4555 21.3571 21.2603 21.194 21.1446 21.1144u11 11.1295 11.2429 11.3066 11.9962 20.6177 23.0888 23.5996 23.602523.4702 23.3435 23.2559 23.1917 23.1505 u12 13.3129 13.3994 13.278913.5349 22.654 25.265 25.8011 25.7794 25.6052 25.4431 25.3306 25.248325.1935 u13 13.316 13.4449 13.5855 14.661 24.5975 27.4555 28.038727.9889 27.7649 27.5612 27.4193 27.3164 27.2455 u14 15.5542 15.610315.4321 16.1384 26.6918 29.7155 30.3242 30.2341 29.9519 29.6994 29.523129.3957 29.3073 u15 15.58 15.7567 16.0956 17.4614 28.7572 32.013732.6572 32.518 32.1673 31.8602 31.6441 31.4885 31.3787 u16 17.88717.8671 17.8082 18.9525 30.94 34.3846 35.0455 34.8442 34.4149 34.045133.7833 33.5958 33.4606 u17 17.9845 18.2619 18.9235 20.4071 33.145836.8156 37.4911 37.2161 36.6987 36.2565 35.9437 35.7192 35.5554 u1820.2884 20.2456 20.5488 21.964 35.4548 39.3279 40.0014 39.6382 39.020638.4973 38.1256 37.8593 37.6646 u19 20.6026 21.1199 21.993 23.544137.8295 41.9212 42.5806 42.1143 41.383 40.7696 40.3329 40.0202 39.7891u20 22.8105 22.9898 23.6434 25.2095 40.3124 44.6095 45.2363 44.649543.79 43.0773 42.5661 42.2016 41.9315 u21 23.6105 24.4211 25.302126.9381 42.8978 47.3978 47.9743 47.2486 46.2474 45.4239 44.8319 44.40744.0928 u22 25.7141 26.2598 27.0831 28.76 45.609 50.2974 50.8009 49.916848.7598 47.8129 47.1293 46.6391 46.2746 u23 27.2209 28.0726 28.95130.6768 48.453 53.3172 53.7241 52.6624 51.3323 50.249 49.4658 48.900148.4795 u24 29.302 30.0719 30.9486 32.7041 51.4455 56.4693 56.754455.4931 53.9725 52.7382 51.8433 51.1958 50.7105 u25 31.3751 32.20933.0801 34.8521 54.6007 59.7663 59.9029 58.419 56.6876 55.2875 54.270253.5266 52.974 u26 33.7153 34.532 35.3703 37.136 57.9366 63.2251 63.185661.4525 59.489 57.9066 56.7507 55.9047 55.2723 u27 36.2816 37.068437.8335 39.572 61.4759 66.868 66.6219 64.6108 62.39 60.607 59.297658.3332 57.6109 u28 39.1419 39.8412 40.4977 42.1824 65.2512 70.727570.2394 67.918 65.413 63.4057 61.9235 60.8256 60.0019 u29 42.336 42.894343.4022 45.0041 69.3127 74.8524 74.0829 71.4105 68.5885 66.3283 64.648763.4014 62.4582 u30 45.9471 46.3002 46.6146 48.1025 73.7506 79.327778.2264 75.1519 71.9717 69.4194 67.5124 66.0884 65.0072 u31 50.180650.2503 50.2989 51.6274 78.7737 84.3532 82.8441 79.2912 75.6839 72.783470.6068 68.9588 67.7069e4) 4096-QAM/64-PAM for a Fading Channel (2. Option)

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9963 0.9978 1.0042 1.00180.9993 1.0199 1.0097 1.0072 1.0028 0.9994 0.9999 0.9996 1.0002 1.0005 u20.9888 0.995 1.0058 1.0009 1 1.0401 1.0467 1.0288 1.0323 1.0103 1.00360.9995 1 1.0007 u3 0.9918 0.9943 1.0101 1.0036 1.0003 1.0198 1.03371.018 1.0303 1.0099 1.0047 0.9997 1.0001 1.0009 u4 0.9541 0.9962 0.99550.9907 1.0023 1.0376 1.0885 1.0841 1.0665 1.0416 1.0207 1.0048 0.99580.9914 u5 0.9509 0.9947 0.9963 0.9911 1.0019 1.0575 1.1007 1.0947 1.06871.0415 1.0205 1.0045 0.9959 0.9919 u6 0.9572 0.994 1.0008 0.9947 1.00081.0371 1.0611 1.0713 1.0375 1.0295 1.018 1.0044 0.9963 0.9921 u7 0.96010.9933 1.0043 0.998 0.9999 1.0167 1.049 1.061 1.0352 1.0293 1.01911.0045 0.9965 0.9922 u8 0.8508 0.9904 1.0057 0.9981 1.0011 1.0359 1.10571.2062 1.3196 1.4848 1.7124 1.9789 2.2284 2.4296 u9 0.8497 0.9921 1.00360.9975 1.0009 1.0568 1.1177 1.2173 1.323 1.4854 1.7111 1.9774 2.2292.4304 u10 0.8453 0.9927 0.9998 0.9957 1.0008 1.0777 1.1579 1.24371.3637 1.5033 1.7169 1.977 2.2279 2.4297 u11 0.8497 0.9966 0.9966 0.99451.0008 1.0584 1.1449 1.2318 1.3601 1.5036 1.7176 1.9772 2.2285 2.4298u12 0.8794 0.9961 1.0066 1.0036 0.9997 1.04 1.0892 1.1572 1.3143 1.4561.6837 1.9674 2.2398 2.4752 u13 0.8775 0.9967 1.0043 1.0016 1 1.05981.1014 1.1687 1.3174 1.4567 1.6825 1.9661 2.2404 2.4761 u14 0.88380.9993 1.0044 1.0026 0.9999 1.0395 1.0619 1.144 1.2769 1.4404 1.67641.9651 2.2423 2.4776 u15 0.887 1.0004 1.0046 1.0026 1.0005 1.0192 1.051.1336 1.2731 1.4409 1.6771 1.9652 2.2428 2.4777 u16 1.3685 2.044 2.42332.7677 2.9386 3.5023 3.4408 3.2474 3.2673 3.4167 3.6611 3.9531 4.22934.4538 u17 1.3632 2.0409 2.4206 2.7543 2.926 3.031 3.3601 3.2589 3.29533.4403 3.6759 3.9601 4.2313 4.4531 u18 1.3522 2.036 2.4072 2.7164 2.86592.7928 3.1046 3.2433 3.3198 3.4991 3.737 4.0075 4.2628 4.4661 u19 1.35842.0387 2.4131 2.7296 2.876 3.0328 3.1327 3.2291 3.2928 3.4736 3.72153.9997 4.2609 4.4673 u20 1.2937 2.0217 2.3696 2.6067 2.872 2.7985 2.88943.0788 3.3078 3.5536 3.8874 4.2677 4.632 4.955 u21 1.2893 2.0179 2.36542.5953 2.8622 2.6481 2.879 3.0908 3.3328 3.5791 3.9074 4.2792 4.63694.954 u22 1.3005 2.0217 2.3804 2.6264 2.9212 2.7978 2.9999 3.0955 3.31143.5221 3.8387 4.2143 4.5858 4.9287 u23 1.3059 2.0243 2.3849 2.63772.9333 3.0347 3.0216 3.0827 3.286 3.4971 3.8215 4.2031 4.5824 4.9304 u241.536 2.0277 2.3595 2.6209 2.931 3.5055 3.4745 3.7641 4.5388 4.80125.2768 5.7983 6.2845 6.6904 u25 1.5286 2.0274 2.3608 2.611 2.9209 3.02943.3939 3.7415 4.5688 4.8766 5.3692 5.8801 6.3465 6.73 u26 1.5142 2.02632.351 2.5814 2.8639 2.7958 3.1184 3.6371 4.2838 4.7955 5.3854 5.99676.555 7.028 u27 1.5207 2.0302 2.3596 2.5937 2.8759 3.0301 3.1528 3.64714.2441 4.7386 5.3092 5.9145 6.4785 6.9667 u28 1.6081 2.0374 2.397 2.71372.8798 3.4906 3.7542 4.4918 4.6545 5.4141 6.1357 6.9502 7.6934 8.3177u29 1.5999 2.0376 2.3962 2.7007 2.8677 3.0254 3.6131 4.3043 4.6739 5.4276.2138 7.0723 7.8706 8.5561 u30 1.6138 2.0443 2.4108 2.7391 2.92743.4965 4.488 4.9563 5.6429 6.2434 7.0601 7.9787 8.901 9.7418 u31 1.62032.0495 2.4173 2.752 2.9369 5.0575 5.6783 6.2681 6.9732 7.6928 8.59419.597 10.5869 11.4949 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u11.0004 1.0002 1.0002 0.9998 0.999 0.9988 0.9995 0.9999 1.0013 0.99991.001 0.9997 1.0009 0.9992 u2 1.0009 0.9991 0.9984 0.9984 1.0001 0.99960.9992 1.0004 1.0032 1.0364 1.3959 1.9271 2.272 2.494 u3 1.0008 0.99920.9986 0.9983 0.9997 0.998 0.9988 1.0013 1.0018 1.037 1.3944 1.92642.2732 2.4945 u4 0.9953 1.0125 1.067 1.2356 1.6294 2.0374 2.3337 2.53412.6647 2.7604 3.1499 3.7388 4.1332 4.3943 u5 0.9956 1.0127 1.067 1.23541.6298 2.0374 2.3334 2.5347 2.6639 2.7604 3.1496 3.7379 4.1327 4.3952 u60.9956 1.0133 1.0683 1.2372 1.6304 2.0374 2.3318 2.5328 2.6769 2.85363.6527 4.7448 5.4651 5.9409 u7 0.9957 1.0135 1.0683 1.2366 1.6304 2.03662.3321 2.5362 2.6761 2.8534 3.6538 4.7432 5.4655 5.9407 u8 2.5769 2.67742.7777 2.9864 3.4541 3.93 4.2773 4.5077 4.6411 4.7342 5.5345 6.71587.4777 7.9756 u9 2.5774 2.6773 2.7771 2.9867 3.4539 3.931 4.2766 4.50894.6405 4.7345 5.5352 6.7145 7.478 7.9745 u10 2.5794 2.6833 2.784 2.99063.4555 3.9297 4.2772 4.5202 4.7063 5.0028 6.2647 7.8812 8.9382 9.6301u11 2.5793 2.6837 2.7837 2.9912 3.4561 3.9294 4.2768 4.5204 4.70615.0025 6.2637 7.8827 8.9384 9.6296 u12 2.6756 2.8656 3.1097 3.58584.4555 5.277 5.8584 6.2318 6.4228 6.6184 7.9618 9.7611 10.9166 11.6754u13 2.6764 2.8653 3.1091 3.5859 4.4552 5.2757 5.8595 6.2314 6.42256.6189 7.9616 9.7632 10.9185 11.6664 u14 2.6747 2.8576 3.1006 3.5774.4507 5.2792 5.8832 6.3219 6.6852 7.215 8.9989 11.1777 12.5855 13.5279u15 2.6746 2.8581 3.1004 3.5775 4.4509 5.2795 5.8851 6.3212 6.68427.2149 8.9993 11.1786 12.5908 13.4849 u16 4.6252 4.7674 4.9751 5.4746.4759 7.4011 8.0147 8.3718 8.5777 8.9581 10.8873 13.2883 14.794415.8428 u17 4.6243 4.7676 4.9767 5.4757 6.4751 7.3997 8.0136 8.3728.5775 8.9585 10.885 13.2918 14.8184 15.6955 u18 4.6188 4.7505 4.95855.4675 6.4921 7.4646 8.1858 8.7429 9.2532 9.94 12.2345 14.9831 16.680518.0725 u19 4.62 4.7491 4.9578 5.4681 6.4921 7.4665 8.1853 8.7398 9.25259.9394 12.2364 15.0095 16.8025 17.6716 u20 5.246 5.5472 5.9566 6.70288.0145 9.1828 9.9708 10.5001 10.9359 11.5978 14.1236 17.1287 18.913120.8359 u21 5.2441 5.5486 5.9602 6.7104 8.0232 9.1919 9.9745 10.499910.9341 11.6041 14.1646 17.2749 19.325 20.0208 u22 5.2556 5.6032 6.06376.8816 8.3055 9.641 10.6757 11.4966 12.1712 12.9965 15.8137 19.128121.168 23.862 u23 5.2584 5.602 6.0592 6.8738 8.2927 9.6278 10.667111.5018 12.202 13.088 16.0518 19.6555 22.0945 22.6034 u24 7.0279 7.34627.7844 8.6613 10.2586 11.7039 12.7329 13.483 14.0789 14.878 17.982621.7256 24.1425 27.5194 u25 7.0459 7.3437 7.7662 8.6344 10.2325 11.691312.7532 13.5672 14.2758 15.2586 18.6869 22.8323 25.575 25.8754 u267.4305 7.8203 8.3639 9.4101 11.2613 12.9619 14.2091 15.1187 15.836916.8096 20.4248 24.7955 27.6541 31.8142 u27 7.3941 7.8194 8.4057 9.502711.4236 13.2128 14.5744 15.6519 16.6054 17.8237 21.8049 26.5569 29.656729.6686 u28 8.8516 9.3478 9.9831 11.1654 13.2585 15.161 16.5544 17.609818.5 19.6965 23.9472 29.0147 32.2679 37.1329 u29 9.1461 9.7003 10.417111.7322 14.0437 16.204 17.8423 19.1046 20.1574 21.4926 26.1156 31.583135.0526 34.4897 u30 10.4828 11.1807 12.0295 13.5243 16.1109 18.480420.2275 21.5413 22.6144 23.9997 29.0224 34.929 38.6023 41.5575 u3112.3176 13.1061 14.0796 15.7967 18.7604 21.4433 23.3683 24.7641 25.866327.2995 32.8238 39.2987 43.2007 45.9849 SNR 28 29 30 31 32 33 34 35 3637 38 39 40 u1 1.0006 1.0043 1.4608 2.031 2.3634 2.5782 2.7135 2.80072.8562 2.8925 2.9145 2.932 2.9432 u2 2.6454 2.7379 3.2219 3.8448 4.22554.4775 4.6426 4.7502 4.8197 4.8656 4.8927 4.9155 4.9282 u3 2.6449 2.7463.6983 4.8763 5.5926 6.0595 6.3617 6.5573 6.6818 6.7624 6.8134 6.85246.8778 u4 4.5762 4.6828 5.6197 6.8402 7.5722 8.051 8.3598 8.5611 8.68788.7697 8.8219 8.8609 8.8865 u5 4.5757 4.7079 6.1651 7.912 8.9681 9.658310.0999 10.3859 10.5661 10.6838 10.7566 10.8106 10.8472 u6 6.2598 6.43657.8821 9.7373 10.8558 11.5914 12.0627 12.3691 12.5612 12.6874 12.76312.8207 12.8615 u7 6.2627 6.5065 8.5398 10.8859 12.31 13.2454 13.841314.2281 14.47 14.6273 14.7205 14.7934 14.8444 u8 8.3042 8.4445 10.431512.8891 14.3481 15.3017 15.9032 16.2913 16.5325 16.6862 16.7743 16.846916.8975 u9 8.3131 8.6065 11.2028 14.1091 15.8609 17.0043 17.7263 18.188918.4766 18.6587 18.7627 18.8479 18.907 u10 10.0729 10.254 12.883315.9704 17.8101 19.0084 19.7625 20.244 20.5396 20.7276 20.8283 20.915120.9752 u11 10.1062 10.5627 13.7734 17.2797 19.3987 20.7764 21.643122.1941 22.5302 22.7431 22.8571 22.9529 23.0199 u12 12.1078 12.302515.599 19.2948 21.4876 22.9043 23.7857 24.3407 24.6737 24.8824 24.988325.0776 25.1403 u13 12.2211 12.8281 16.6269 20.7185 23.1709 24.755425.7402 26.3568 26.7257 26.9539 27.0702 27.1641 27.23 u14 13.978714.3539 18.3392 22.6727 25.2367 26.8878 27.9051 28.5338 28.9056 29.131629.2408 29.3276 29.3905 u15 14.2723 15.1126 19.5353 24.2439 27.047128.8505 29.9595 30.6383 31.0373 31.2752 31.3895 31.4767 31.5389 u1616.1851 16.7817 21.4333 26.3916 29.2986 31.147 32.2702 32.9453 33.330633.5558 33.6536 33.727 33.7773 u17 16.7562 17.7277 22.7796 28.106231.2381 33.2292 34.4336 35.1516 35.5544 35.7864 35.8824 35.9518 35.997u18 18.3851 19.2664 24.6112 30.2335 33.5042 35.5666 36.7993 37.522837.9155 38.1359 38.2116 38.2677 38.2999 u19 19.2499 20.3968 26.132332.1242 35.6097 37.8022 39.1019 39.8565 40.2573 40.4733 40.5406 40.588240.6091 u20 21.0165 22.1002 28.1574 34.4644 38.0874 40.3385 41.651342.3946 42.7722 42.9647 43.0011 43.0265 43.0262 u21 22.1679 23.430629.8838 36.5679 40.3963 42.7627 44.1297 44.8896 45.2621 45.4415 45.458945.4682 45.4529 u22 23.9006 25.1704 31.9904 39.027 43.0119 45.448246.8305 47.576 47.92 48.069 48.0512 48.0322 47.99 u23 25.3642 26.755633.9846 41.4123 45.5943 48.1289 49.5435 50.2892 50.6125 50.7335 50.684450.639 50.5714 u24 27.3645 28.7536 36.3885 44.2002 48.5385 51.127252.5353 53.2485 53.5222 53.5931 53.4946 53.4105 53.3077 u25 29.148430.6214 38.698 46.9287 51.4594 54.1327 55.5551 56.2467 56.4806 56.511956.3625 56.2412 56.1041 u26 31.3343 32.829 41.3722 50.0315 54.73457.4607 58.8707 59.512 59.683 59.6552 59.4393 59.268 59.0883 u27 33.564835.1146 44.1486 53.2678 58.1622 60.9496 62.3471 62.9389 63.0415 62.945462.6599 62.439 62.2059 u28 36.2682 37.8272 47.3995 57.0085 62.083964.905 66.2558 66.7683 66.7757 66.5764 66.2081 65.9151 65.6227 u2939.1974 40.7685 50.93 61.0847 66.3515 69.2122 70.5087 70.932 70.8370.5214 70.0572 69.6802 69.3125 u30 42.8228 44.3725 55.219 65.990371.458 74.3362 75.5397 75.8248 75.5766 75.0956 74.5263 74.0405 73.5803u31 47.4691 48.9596 60.6605 72.1993 77.8935 80.7711 81.8379 81.928681.4804 80.7898 80.0683 79.4178 78.8141f1) 16384-QAM/128-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 1 0.9993 1 0.9983 1.0007 1.00151.0005 1.034 0.9706 0.9792 0.9884 0.9946 1 1.0017 u2 0.9996 0.99660.9973 0.9973 1.0014 1.0022 1.0008 1.0677 1.0314 0.9448 0.9812 0.9870.9986 1.0025 u3 0.9997 0.9957 0.9967 0.9982 1.0024 1.0036 1.0013 1.03651.0638 0.9658 0.9922 0.9931 0.9987 1.0014 u4 0.9989 0.9931 0.9864 0.9911.0016 1.0036 1.0011 1.0667 1.1349 1.0711 0.9776 0.9939 0.9879 0.9959 u50.9989 0.9922 0.9863 0.9895 1.0024 1.0048 1.001 1.0998 1.0995 1.04740.9662 0.989 0.9878 0.9977 u6 0.9993 0.9922 0.9882 0.99 1.0037 1.00571.001 1.0673 1.0313 1.0874 0.973 0.9976 0.9894 0.9975 u7 0.9993 0.99160.9875 0.9909 1.0047 1.0072 1.001 1.0344 1.0642 1.111 0.984 1.00340.9894 0.9963 u8 0.9951 0.9917 0.9456 0.9589 0.9962 0.9983 1.0007 1.0671.1363 1.2505 1.0822 1.0041 0.9777 0.9679 u9 0.9951 0.9914 0.9455 0.95770.9964 0.9989 1.0003 1.1002 1.1015 1.2244 1.0692 0.9982 0.9776 0.9695u10 0.9947 0.9897 0.9433 0.9569 0.9964 0.9991 1.0003 1.1343 1.17381.1804 1.0619 0.9896 0.9761 0.9704 u11 0.9948 0.9893 0.9427 0.9579 0.9970.9997 1.0005 1.1 1.2107 1.2066 1.0748 0.9955 0.9761 0.9693 u12 0.99570.9901 0.9516 0.9639 0.9992 1.0016 1.0001 1.0653 1.135 1.0796 1.0940.995 0.9867 0.9751 u13 0.9956 0.9895 0.9517 0.9627 0.9995 1.0023 1.00041.0987 1.0997 1.0561 1.0806 0.9892 0.9865 0.9767 u14 0.996 0.9899 0.95350.9633 1.0005 1.0031 1.0014 1.0659 1.0325 1.0964 1.0878 0.9976 0.9880.9764 u15 0.9961 0.9895 0.953 0.9642 1.0011 1.0037 1.0025 1.0336 1.06581.1205 1.1011 1.0033 0.9881 0.9754 u16 0.9984 0.9899 0.8171 0.85461.0039 1.0033 0.9981 1.0672 1.1362 1.2542 1.5262 1.8221 2.2124 2.5552u17 0.998 0.9881 0.8182 0.8543 1.0029 1.003 0.9991 1.1011 1.1004 1.22661.5101 1.8088 2.2165 2.5557 u18 0.9973 0.9857 0.8174 0.8547 1.00211.0026 1.0001 1.1349 1.1725 1.1819 1.5083 1.792 2.2072 2.5533 u19 0.9970.9839 0.8178 0.8565 1.0014 1.002 1.0005 1.1002 1.2089 1.2075 1.52521.8052 2.2032 2.5518 u20 0.9959 0.9826 0.8116 0.8518 0.9992 1.00151.0022 1.1352 1.2878 1.3476 1.5028 1.8306 2.2015 2.5399 u21 0.99540.9808 0.8125 0.8518 0.9982 1.0008 1.0025 1.17 1.2499 1.3196 1.48611.8168 2.2056 2.5406 u22 0.9955 0.9789 0.815 0.8533 0.9979 1 1.00261.135 1.1725 1.3648 1.4886 1.8343 2.215 2.5421 u23 0.9952 0.9769 0.81560.8551 0.9971 0.9994 1.0024 1.1007 1.2087 1.3912 1.5052 1.8483 2.21062.5402 u24 1.0005 0.9931 0.845 0.8795 1.0034 1.0026 0.9971 1.0677 1.13531.2436 1.3577 1.8233 2.2108 2.5682 u25 1.0003 0.9929 0.8454 0.879 1.00311.0023 0.9974 1.1013 1.0999 1.2172 1.3421 1.8099 2.2148 2.569 u26 0.99970.9917 0.844 0.8788 1.0024 1.0022 0.9976 1.1352 1.1719 1.1732 1.33711.7933 2.2056 2.5669 u27 0.9996 0.9914 0.8441 0.8798 1.0023 1.00220.9975 1.1008 1.2084 1.1991 1.3532 1.8066 2.2015 2.5654 u28 1.00040.9915 0.8515 0.8852 1.0043 1.003 0.997 1.0669 1.1327 1.073 1.37521.7831 2.2028 2.5752 u29 1.0003 0.9914 0.8517 0.8845 1.0042 1.00270.9971 1.1002 1.0976 1.0498 1.3592 1.7703 2.2067 2.5759 u30 1.00060.9923 0.8534 0.8853 1.0047 1.0027 0.9971 1.0673 1.031 1.09 1.36391.7861 2.2154 2.5775 u31 1.0005 0.9922 0.8533 0.8861 1.0048 1.003 0.99711.0348 1.0641 1.1142 1.3795 1.7986 2.2115 2.576 u32 1.001 0.9912 1.30491.8562 2.8726 3.3437 3.6766 4.4164 4.2323 3.9974 3.6762 3.9437 4.34344.6869 u33 1.001 0.9912 1.3059 1.8533 2.8736 3.3442 3.6763 4.0344 4.68574.1775 3.7129 3.94 4.3617 4.6707 u34 1.0007 0.9901 1.3027 1.8523 2.87093.3444 3.6755 3.8268 4.129 4.544 3.8489 3.9531 4.3441 4.6549 u35 1.00080.99 1.3027 1.8562 2.8735 3.3451 3.6754 4.0296 3.8985 4.3272 3.80333.9572 4.3254 4.6714 u36 1 0.9898 1.288 1.8394 2.8539 3.3416 3.67273.8227 3.7104 3.8963 3.8829 4.0881 4.4848 4.7175 u37 1.0001 0.99 1.28911.8368 2.8544 3.3419 3.6724 3.682 3.8598 4.0066 3.9374 4.088 4.50434.7001 u38 1.0007 0.991 1.2929 1.8392 2.8609 3.3431 3.6733 3.8219 4.11653.8085 3.7902 4.0676 4.519 4.7173 u39 1.0008 0.9911 1.293 1.8431 2.86323.3439 3.6733 4.0286 3.887 3.7183 3.7456 4.0679 4.5003 4.7354 u40 0.99610.9714 1.2251 1.7528 2.8145 3.3394 3.6733 3.8208 3.7067 3.5597 3.71614.1938 4.6751 5.1297 u41 0.9963 0.9726 1.2262 1.7507 2.8144 3.33943.6727 3.6829 3.86 3.6216 3.7475 4.1977 4.6923 5.1059 u42 0.9963 0.97351.2238 1.7496 2.8118 3.3391 3.6711 3.5697 3.7022 3.7482 3.8547 4.22444.6842 5.0907 u43 0.9966 0.9749 1.2239 1.7533 2.8135 3.3395 3.6709 3.6813.5841 3.681 3.8177 4.2197 4.6663 5.1147 u44 0.9977 0.9754 1.2383 1.76962.8355 3.3437 3.6752 3.8266 3.7152 3.8707 3.7599 4.0885 4.4867 5.034 u450.998 0.977 1.2392 1.7673 2.8354 3.3437 3.6748 3.681 3.8683 3.97793.7926 4.0884 4.506 5.0119 u46 0.9987 0.9788 1.2429 1.7696 2.8409 3.34463.6759 3.8263 4.1241 3.783 3.6924 4.0692 4.5205 5.0277 u47 0.9991 0.97991.2432 1.7733 2.843 3.3451 3.6758 4.0358 3.8954 3.6969 3.6664 4.06944.502 5.0496 u48 0.9972 0.9797 1.5256 2.1641 2.8191 3.3379 3.674 4.44834.2332 3.9685 4.3926 5.9305 7.0157 7.1789 u49 0.997 0.9815 1.5258 2.15952.8191 3.3376 3.6737 4.0435 4.6652 4.1389 4.5191 6.1718 6.8164 7.2237u50 0.9964 0.9819 1.5208 2.1572 2.8158 3.3365 3.672 3.8308 4.1164 4.54.6254 6.4012 7.1426 7.4095 u51 0.9964 0.9832 1.5197 2.1616 2.81773.3369 3.6723 4.0414 3.8933 4.2885 4.5203 6.1766 7.3723 7.3415 u520.9954 0.985 1.5005 2.1393 2.7992 3.3311 3.6667 3.8285 3.707 3.8764.6675 5.8214 6.8937 7.469 u53 0.9952 0.9859 1.5008 2.135 2.7992 3.33153.6667 3.6836 3.8623 3.9845 4.7729 5.9508 6.7776 7.5359 u54 0.99560.9877 1.5048 2.1374 2.8044 3.3331 3.6686 3.8296 4.1085 3.7906 4.72065.7884 6.5877 7.3703 u55 0.9955 0.9883 1.5038 2.1418 2.8065 3.3336 3.6694.0381 3.8823 3.7034 4.578 5.6671 6.6852 7.3203 u56 1.0003 0.9856 1.59862.2732 2.8502 3.3457 3.6758 4.4277 4.2272 4.0107 6.8098 5.9404 7.02818.3261 u57 1.0001 0.9875 1.5984 2.268 2.8488 3.3444 3.6743 4.0363 4.64824.1891 6.6195 6.1853 6.8253 8.6598 u58 0.9996 0.9889 1.5931 2.26512.8447 3.3415 3.6721 3.8297 4.1163 4.5614 5.7764 6.4179 7.1544 8.8641u59 0.9995 0.9906 1.5917 2.2696 2.8451 3.3406 3.6715 4.0351 3.88974.3447 5.6596 6.191 7.3852 8.5998 u60 1.0002 0.9943 1.6107 2.2933 2.86163.3435 3.6769 4.4379 4.2418 6.2574 5.5599 7.6849 8.8055 9.6276 u61 10.9974 1.6105 2.288 2.86 3.3413 3.6755 4.0431 4.6809 6.1223 5.73917.6587 8.6932 9.9296 u62 1.0004 1.0005 1.6144 2.29 2.8621 3.3393 3.67594.4373 6.7937 7.0647 7.3527 8.496 11.6838 11.0046 u63 1.0003 1.00331.6124 2.2943 2.8617 3.3378 3.6747 8.1118 8.3013 8.3718 9.0057 10.32099.854 13.0332 SNR 14 15 16 17 18 19 20 21 22 23 24 25 26 27 u1 1.00080.9999 1 1 0.9994 1.0003 0.9999 1 1.0003 1.0007 1.0007 1.0007 0.99961.0009 u2 1.0009 0.9999 0.9999 1.0005 1.0005 1.0006 0.9998 1.0002 1.00051.0011 1.0006 0.9993 1.0002 1.0011 u3 1.0001 0.9998 0.9998 1.0006 1.00051.0005 0.9997 0.9998 1.001 1.0015 1.0002 0.9982 1.0007 1.0003 u4 1.00011.0016 0.9993 0.9948 0.9943 0.999 1.0007 1.0014 1.0008 1.0007 1.01351.0874 1.8839 2.7462 u5 1.0009 1.0016 0.9993 0.9947 0.9939 0.9991 1.00061.001 1.0009 1.0009 1.0138 1.0879 1.8845 2.7474 u6 1.0007 1.0011 0.99920.9942 0.9924 0.9988 1.0006 1.0004 1.0003 1.0012 1.014 1.0882 1.88372.7463 u7 0.9998 1.001 0.9991 0.9942 0.9925 0.9987 1.0006 1.0007 1.00091.0005 1.0135 1.0873 1.8837 2.7459 u8 0.9689 0.9815 1.0058 1.0493 1.1691.5305 2.4126 2.8284 2.9665 3.0033 3.0148 3.0589 3.8561 4.7555 u9 0.96970.9815 1.0056 1.0492 1.1687 1.5304 2.4125 2.8278 2.9664 3.0033 3.0153.059 3.8562 4.7559 u10 0.9699 0.9817 1.0055 1.0496 1.1698 1.5307 2.41192.8286 2.9669 3.0036 3.0148 3.0584 3.8562 4.7561 u11 0.9691 0.98161.0055 1.0497 1.1699 1.5305 2.4118 2.8292 2.9669 3.0034 3.0149 3.05863.854 4.7547 u12 0.969 0.9797 1.0057 1.0551 1.1775 1.5327 2.4121 2.82882.9668 3.0111 3.0576 3.2441 4.9271 6.5695 u13 0.9697 0.9795 1.0057 1.0551.177 1.5325 2.4116 2.8286 2.9667 3.0107 3.0577 3.2451 4.9274 6.5696 u140.9695 0.9791 1.0056 1.0546 1.1755 1.5323 2.412 2.8275 2.9669 3.01083.0577 3.2451 4.9282 6.5694 u15 0.9687 0.979 1.0055 1.0548 1.1753 1.53232.412 2.8271 2.9668 3.0108 3.0581 3.245 4.9282 6.5697 u16 2.7702 2.89742.9701 3.0217 3.1155 3.4884 4.4446 4.891 5.0389 5.064 5.0544 5.12566.8448 8.6152 u17 2.7733 2.8969 2.9697 3.0221 3.1156 3.4886 4.44394.8918 5.0381 5.0641 5.0537 5.1247 6.8437 8.6127 u18 2.7713 2.8988 2.9693.0187 3.1129 3.4886 4.4435 4.892 5.0384 5.0647 5.0539 5.1251 6.84368.6136 u19 2.768 2.8987 2.9692 3.0184 3.1123 3.4889 4.4445 4.8915 5.03895.0642 5.0546 5.1254 6.8444 8.6151 u20 2.7659 2.9081 2.9906 3.04653.1292 3.4897 4.4403 4.8898 5.048 5.1086 5.2014 5.57 8.2168 10.5563 u212.7689 2.9078 2.9902 3.0468 3.1296 3.4901 4.4402 4.8888 5.0476 5.10855.2016 5.5695 8.2162 10.5568 u22 2.7708 2.9054 2.9907 3.0504 3.1321 3.494.4409 4.8892 5.0476 5.1089 5.2009 5.5697 8.2161 10.5567 u23 2.76762.9054 2.9909 3.05 3.1314 3.49 4.4408 4.8892 5.0481 5.1088 5.2021 5.56988.2162 10.5562 u24 2.8379 3.0215 3.1624 3.3145 3.6255 4.4521 6.16786.9242 7.1628 7.1826 7.1349 7.3211 10.1056 12.6823 u25 2.8408 3.02133.1619 3.3148 3.6262 4.4522 6.1674 6.9248 7.1627 7.1825 7.1349 7.322410.1062 12.6839 u26 2.8388 3.0232 3.1612 3.3105 3.6215 4.4505 6.1676.9249 7.1626 7.181 7.1341 7.3213 10.1065 12.6838 u27 2.8358 3.02313.1614 3.3101 3.6205 4.4502 6.1672 6.924 7.1629 7.1809 7.1352 7.322610.1051 12.6818 u28 2.8379 3.0146 3.1396 3.276 3.5926 4.4391 6.16586.9478 7.2373 7.3699 7.5672 8.2272 11.7834 14.8109 u29 2.8408 3.01423.1392 3.2764 3.5931 4.4392 6.1658 6.9479 7.2365 7.3696 7.5675 8.226811.784 14.8118 u30 2.8427 3.012 3.1397 3.2807 3.5971 4.4406 6.16596.9475 7.2381 7.3713 7.5677 8.2255 11.7837 14.8121 u31 2.8398 3.01183.1399 3.2804 3.5959 4.4403 6.1655 6.9471 7.2382 7.3713 7.5673 8.226511.7838 14.8114 u32 4.905 5.0812 5.2135 5.325 5.5623 6.4222 8.34249.1832 9.4264 9.4043 9.3988 9.8918 13.7405 17.0945 u33 4.8974 5.08295.215 5.3243 5.5612 6.4225 8.3441 9.1835 9.4249 9.4037 9.3995 9.892513.7398 17.0938 u34 4.8874 5.076 5.2182 5.3348 5.5671 6.4201 8.3389.1798 9.4272 9.4071 9.4006 9.891 13.7388 17.1031 u35 4.8948 5.07415.2166 5.3355 5.568 6.42 8.3361 9.179 9.4282 9.4051 9.4001 9.891513.7404 17.1045 u36 4.885 5.0286 5.1483 5.2618 5.5314 6.4329 8.40499.3505 9.749 9.9946 10.3826 11.2919 15.7071 19.4613 u37 4.8776 5.03035.1496 5.2612 5.5306 6.4335 8.4058 9.3517 9.7493 9.9944 10.383 11.290915.7076 19.4608 u38 4.8877 5.0366 5.1467 5.2526 5.5259 6.435 8.41189.3554 9.7463 9.9884 10.3801 11.2952 15.7218 19.5261 u39 4.8951 5.03495.1452 5.2532 5.5266 6.4346 8.4112 9.3542 9.7462 9.9877 10.3803 11.29615.7228 19.5267 u40 5.4496 5.6707 5.8312 6.0427 6.6485 8.0446 10.535611.5836 11.9143 11.9816 12.1731 12.9935 17.8481 21.9597 u41 5.42655.6719 5.834 6.0408 6.6435 8.0389 10.529 11.5843 11.9143 11.9825 12.173312.9944 17.8484 21.9601 u42 5.4225 5.6558 5.8389 6.0682 6.6777 8.075810.564 11.594 11.9068 11.9727 12.1767 13.0275 17.9412 22.2188 u43 5.44625.6536 5.8354 6.0699 6.6825 8.0813 10.57 11.5945 11.9058 11.9725 12.176813.0261 17.9437 22.2189 u44 5.4486 5.7255 5.982 6.2744 6.9056 8.350810.998 12.2939 12.8674 13.2919 13.7704 14.7383 20.0927 24.5954 u455.4255 5.7265 5.9847 6.2728 6.9005 8.3443 10.9898 12.2904 12.8677 13.29313.7699 14.7365 20.0925 24.596 u46 5.4293 5.7408 5.9804 6.2474 6.86618.3021 10.9418 12.2656 12.878 13.3338 13.851 14.9101 20.458 25.3588 u475.4516 5.7388 5.9771 6.2491 6.8705 8.3084 10.9501 12.2696 12.878213.3327 13.8513 14.9118 20.459 25.3582 u48 7.6559 7.9191 8.1097 8.28648.8134 10.3614 13.3436 14.6402 15.0909 15.3053 15.6604 16.6484 22.57227.6657 u49 7.5962 7.8987 8.101 8.2903 8.8247 10.3765 13.3569 14.638715.0847 15.3073 15.6653 16.6516 22.5734 27.6641 u50 7.7659 7.9125 8.06788.2301 8.7499 10.2913 13.2832 14.6429 15.1817 15.4954 15.9904 17.212923.5603 29.2694 u51 7.8178 7.9342 8.0761 8.2269 8.7415 10.2787 13.270514.6437 15.1843 15.4947 15.9844 17.2069 23.5559 29.2779 u52 7.99058.3659 8.5924 8.7764 9.3449 11.0377 14.3958 16.258 17.0226 17.378917.8016 18.9547 25.6725 31.5778 u53 7.9568 8.3388 8.5733 8.7818 9.368511.0789 14.4533 16.308 17.0397 17.3723 17.7872 18.9473 25.6812 31.6373u54 7.7652 8.2889 8.6071 8.8942 9.5447 11.3315 14.8025 16.7236 17.631818.1013 18.7148 20.2064 27.4993 33.8765 u55 7.8166 8.3137 8.6248 8.88999.5217 11.2906 14.743 16.6632 17.5973 18.1025 18.7549 20.2774 27.648634.1856 u56 9.5716 10.0368 10.4727 10.7927 11.475 13.4022 17.181619.0526 19.7879 20.1226 20.5974 21.9997 29.7286 36.4886 u57 10.555810.1562 10.4808 10.7507 11.4153 13.3253 17.0826 18.9593 19.7761 20.200420.7571 22.2698 30.256 37.411 u58 10.0469 10.511 10.9283 11.2366 11.923313.9203 17.8741 19.9721 21.162 21.7752 22.4108 23.9661 32.3556 39.7554u59 9.5131 10.3449 10.8696 11.2796 12.0343 14.0983 18.1489 20.347521.6061 22.3479 23.0885 24.8194 33.7387 41.7463 u60 9.5784 11.560312.3311 12.9013 13.7996 16.085 20.5183 22.6963 23.7407 24.31 24.975926.6835 36.0295 44.3668 u61 10.5573 11.9943 12.7965 13.3906 14.299316.6522 21.2455 23.5932 24.9025 25.8342 26.7381 28.6155 38.5765 47.3857u62 12.0078 13.117 14.0906 14.9695 16.1458 18.8287 23.9395 26.410927.5876 28.3405 29.1578 31.0568 41.6691 50.9452 u63 14.393 15.268416.2378 17.167 18.4863 21.5011 27.2192 29.8709 30.9873 31.5842 32.250134.1089 45.4747 55.251 SNR 28 29 30 31 32 33 34 35 36 37 38 39 40 u10.9979 0.9994 0.9996 1.0018 1 0.9958 1.0001 0.9984 1.0002 1.0034 2.35112.8929 2.9812 u2 1.0007 1 0.9994 1.0053 1.2266 2.7568 2.9441 2.99042.9988 3.0035 4.3493 4.8979 4.9814 u3 0.9997 0.9987 0.9994 1.0059 1.22662.7554 2.9418 2.9923 2.9989 3.0068 5.7136 6.7911 6.9665 u4 2.9315 2.98722.9987 3.0069 3.1896 4.7549 4.9513 4.996 5.0029 5.0054 7.7072 8.80028.9696 u5 2.9336 2.9859 2.9982 3.0076 3.189 4.7564 4.949 4.9994 5.00285.0111 9.0998 10.7 10.96 u6 2.9337 2.9866 2.9994 3.0181 3.5189 6.53356.9078 6.9976 7.0097 7.015 11.0829 12.7134 12.9713 u7 2.9334 2.98652.9997 3.0183 3.5182 6.5332 6.9073 6.9995 7.0099 7.0231 12.5168 14.623914.9709 u8 4.9479 5.0032 5.0133 5.0197 5.3804 8.5371 8.928 9.0199 9.02699.0321 14.4903 16.643 16.9909 u9 4.948 5.0038 5.0139 5.0214 5.37998.5369 8.9292 9.0199 9.0271 9.041 15.9681 18.5695 19.0023 u10 4.94695.0038 5.0137 5.0505 5.9287 10.3494 10.9095 11.04 11.052 11.0524 17.936620.5989 21.033 u11 4.9474 5.0063 5.015 5.0496 5.9277 10.3496 10.908811.0425 11.0518 11.0678 19.464 22.5427 23.0556 u12 6.9307 7.0326 7.0457.0381 7.657 12.3657 12.9485 13.0857 13.0908 13.0776 21.4254 24.585525.1004 u13 6.9312 7.0319 7.0445 7.0398 7.6568 12.3664 12.9482 13.086813.0908 13.1135 22.9997 26.5489 27.1403 u14 6.9306 7.034 7.0512 7.11618.5075 14.2266 14.9667 15.1374 15.1424 15.1029 24.9582 28.6048 29.2023u15 6.9308 7.0339 7.0507 7.1152 8.5081 14.2263 14.9654 15.1385 15.143215.1828 26.5839 30.5966 31.2639 u16 9.0002 9.1099 9.1078 9.0596 10.119316.2649 17.0437 17.2199 17.2122 17.1228 28.5435 32.6686 33.3472 u17 99.1093 9.1085 9.0594 10.1198 16.2654 17.0432 17.2194 17.2139 17.29330.2168 34.6883 35.4328 u18 9.0014 9.1102 9.1259 9.2488 11.2407 18.188119.1132 19.3127 19.2996 19.1443 32.1825 36.7806 37.5374 u19 9.00089.1102 9.1266 9.2503 11.2404 18.19 19.1131 19.3136 19.3035 19.485633.9092 38.8301 39.6482 u20 11.0793 11.2291 11.1982 11.0923 12.783120.2619 21.2378 21.4435 21.408 21.2084 35.8821 40.9457 41.781 u2111.0811 11.2237 11.1986 11.093 12.7828 20.264 21.2361 21.4438 21.41921.8192 37.6595 43.0323 43.9222 u22 11.08 11.2233 11.2559 11.514 14.080322.2679 23.3688 23.5964 23.535 23.4078 39.6452 45.1778 46.0864 u2311.0799 11.2286 11.2575 11.5138 14.0809 22.2665 23.3675 23.5944 23.56324.3166 41.4777 47.3044 48.262 u24 13.254 13.3977 13.3168 13.220815.6096 24.3937 25.5513 25.7849 25.6784 25.8019 43.484 49.4846 50.4619u25 13.2562 13.4214 13.3181 13.2211 15.6103 24.3918 25.5503 25.783925.7477 26.9208 45.3687 51.6538 52.6767 u26 13.2578 13.4225 13.482814.0047 17.0212 26.4894 27.7584 28.0066 27.8312 28.3524 47.3978 53.873354.9154 u27 13.2556 13.3979 13.4821 14.0052 17.0222 26.487 27.758928.0087 27.9939 29.588 49.3396 56.0924 57.1743 u28 15.5004 15.711115.4632 15.5855 18.577 28.6855 30.0225 30.262 29.9913 31.0147 51.397858.3558 59.4576 u29 15.4857 15.6237 15.4644 15.5855 18.5771 28.684830.0223 30.2757 30.3481 32.3241 53.3977 60.6272 61.764 u30 15.486515.625 15.8754 16.7318 20.086 30.8885 32.3293 32.5545 32.2059 33.761755.4958 62.9378 64.0976 u31 15.5004 15.7115 15.8741 16.7312 20.086430.8896 32.3289 32.5945 32.8891 35.1249 57.5558 65.2691 66.4551 u3217.8171 17.905 17.7218 18.2489 21.6967 33.1813 34.694 34.878 34.602136.5843 59.7015 67.6399 68.843 u33 17.8798 18.1687 17.7224 18.248821.6967 33.1827 34.6962 34.988 35.6555 38.0015 61.8319 70.0352 71.2583u34 17.8811 18.1688 18.5635 19.6203 23.3093 35.5155 37.1099 37.218337.2621 39.4949 64.0329 72.4733 73.7038 u35 17.8183 17.9043 18.560719.6213 23.3086 35.5157 37.1257 37.4866 38.5681 40.965 66.2391 74.943876.1825 u36 20.4505 20.9194 20.2864 21.1594 25.0044 37.9407 39.585839.5997 40.1396 42.5006 68.5084 77.4569 78.6956 u37 20.2235 20.261320.2866 21.1597 25.0041 37.9408 39.6421 40.1825 41.5814 44.0283 70.798580.0072 81.2408 u38 20.2228 20.2596 21.5865 22.686 26.7369 40.431242.1039 42.1382 43.1702 45.6142 73.1434 82.6023 83.8204 u39 20.451420.9191 21.5864 22.6865 26.7378 40.4436 42.272 43.174 44.7056 47.206775.5241 85.2424 86.4403 u40 22.7323 22.8862 23.2637 24.3144 28.546643.0066 44.6578 44.9926 46.3389 48.8473 77.964 87.9349 89.0997 u4123.3691 24.1348 23.2623 24.3135 28.5545 43.0586 45.082 46.4069 47.95950.5165 80.4512 90.6751 91.7963 u42 23.3697 24.133 24.8626 25.986530.4157 45.6368 47.3199 48.1706 49.6546 52.2317 83.0006 93.4666 94.5366u43 22.7335 22.884 24.8623 25.9901 30.4477 45.8192 48.2111 49.802451.365 53.9774 85.6011 96.3129 97.3205 u44 26.8707 27.7628 26.62727.7458 32.3527 48.3313 50.2897 51.5981 53.1407 55.7749 88.2682 99.2175100.1494 u45 25.5392 26.0216 26.6288 27.7722 32.4627 48.8191 51.722853.3748 54.9521 57.6155 91.0021 102.1821 103.0246 u46 25.5384 26.021728.4475 29.5707 34.3386 51.1757 53.7055 55.2549 56.8268 59.5099 93.8041105.2061 105.9496 u47 26.8739 27.7594 28.4692 29.6678 34.6571 52.218655.4999 57.1658 58.754 61.4529 96.6737 108.2976 108.9276 u48 28.985129.7601 30.3758 31.4616 36.4337 54.4329 57.5125 59.1587 60.7475 63.455699.6202 111.4573 111.9612 u49 30.9531 31.7887 30.4711 31.7591 37.164756.0941 59.5286 61.2176 62.8057 65.5158 102.6436 114.6864 115.0528 u5030.9871 31.9024 32.379 33.4641 38.8366 58.2455 61.6737 63.3609 64.937467.6339 105.7482 117.9917 118.2042 u51 28.9841 29.7382 32.6972 34.178640.0745 60.3086 63.8886 65.5921 67.1439 69.821 108.9399 121.3788 121.419u52 36.1367 37.333 34.5326 35.8013 41.7055 62.5724 66.2226 67.917669.4313 72.0776 112.2236 124.848 124.7037 u53 33.1985 33.9707 35.32237.0377 43.2892 64.913 68.6675 70.3445 71.8036 74.4055 115.6037 128.406128.065 u54 33.3646 34.356 37.0884 38.642 45.0343 67.4166 71.239672.8828 74.2672 76.8106 119.0894 132.0584 131.5042 u55 35.5643 36.358438.4975 40.2456 46.8714 70.0657 73.9506 75.5343 76.8264 79.2998 122.6798135.8153 135.0306 u56 39.6646 41.0237 40.2896 42.0186 48.848 72.893176.8123 78.3118 79.4908 81.8779 126.395 139.6847 138.6529 u57 41.8843.1264 42.1523 43.921 50.9695 75.9027 79.8314 81.223 82.2696 84.5537130.2427 143.6811 142.3817 u58 44.1256 45.4315 44.2271 45.9956 53.255379.117 83.0274 84.2827 85.1746 87.3442 134.239 147.8142 146.2294 u5938.3088 39.301 46.5077 48.2517 55.7201 82.5548 86.4123 87.508 88.219990.2591 138.4055 152.109 150.2155 u60 49.7784 50.9441 49.0319 50.714958.3845 86.247 90.03 90.927 91.432 93.3206 142.7773 156.5952 154.3654u61 46.7646 48.0249 51.8299 53.4212 61.2877 90.244 93.9167 94.579294.8467 96.5606 147.3943 161.3181 158.7214 u62 53.972 54.8835 54.975356.4311 64.4959 94.6335 98.1642 98.5339 98.5319 100.0465 152.3396166.3635 163.3522 u63 58.1359 58.7942 58.632 59.9046 68.168 99.6426102.9507 102.9731 102.6388 103.9069 157.8042 171.9112 168.4213f2) 16384-QAM/128-PAM for a Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9989 0.9988 1.0029 1.00231.0009 1.0079 1.0046 1.0005 1.0018 0.9971 0.9989 0.9997 0.9991 1.0004 u20.9962 0.997 1.0044 1.0031 1.0013 1.022 1.0156 1.0084 1.0048 0.99510.9981 0.9994 0.9985 1.0006 u3 0.9967 0.9958 1.0074 1.0046 1.0013 1.01371.0141 1.0096 1.007 0.9954 0.9984 0.9994 0.9979 1.0007 u4 0.9871 0.9941.0057 1.001 1.001 1.0342 1.0501 1.0275 1.0253 1.0156 1.0024 0.99970.9975 1.0011 u5 0.9859 0.9927 1.0082 1.0019 1.0012 1.043 1.0524 1.02681.0263 1.0136 1.0011 0.9995 0.9968 1.0013 u6 0.9879 0.9917 1.0111 1.00451.0011 1.0287 1.0435 1.0193 1.026 1.0138 1.0008 0.9994 0.9963 1.0013 u70.9885 0.9899 1.0138 1.0058 1.0007 1.0207 1.0415 1.0198 1.0271 1.01481.0013 0.9994 0.9958 1.0013 u8 0.9494 0.9964 0.9929 0.9874 1.0002 1.04121.0937 1.0881 1.0715 1.0391 1.0201 1.0035 0.9936 0.9926 u9 0.9484 0.99510.9943 0.9878 1.0002 1.0493 1.0955 1.0876 1.0708 1.038 1.0193 1.00340.9932 0.9928 u10 0.9462 0.9939 0.9943 0.9877 1.0002 1.0636 1.10481.0962 1.0722 1.0369 1.0191 1.0032 0.9925 0.993 u11 0.9468 0.993 0.99620.9887 1.0002 1.0553 1.1012 1.0967 1.0715 1.039 1.0198 1.0033 0.9920.993 u12 0.9552 0.9922 1.0031 0.9949 1.0011 1.0348 1.0609 1.0737 1.0491.0201 1.0156 1.003 0.992 0.9933 u13 0.9542 0.9914 1.0047 0.9955 1.0021.0429 1.0633 1.0732 1.0486 1.0187 1.0147 1.0028 0.9916 0.9934 u140.9561 0.9905 1.0073 0.9983 1.0037 1.0285 1.0536 1.0649 1.0466 1.02021.0148 1.0029 0.9913 0.9934 u15 0.9567 0.9895 1.0089 0.9998 1.006 1.02031.0512 1.0654 1.0463 1.022 1.0154 1.0029 0.9906 0.9934 u16 0.846 0.98721.0079 0.9975 0.9977 1.0393 1.1037 1.2076 1.3294 1.4778 1.7101 1.972.2195 2.4304 u17 0.8463 0.9886 1.0064 0.9978 0.9995 1.0486 1.10821.2067 1.3296 1.4754 1.7087 1.9697 2.2196 2.4307 u18 0.8453 0.99 1.0050.9969 1.0006 1.0635 1.1194 1.216 1.3325 1.4737 1.7084 1.9694 2.21942.4311 u19 0.8467 0.9912 1.0037 0.9969 1.002 1.0559 1.1172 1.2163 1.33221.4759 1.7097 1.9697 2.2194 2.4312 u20 0.8403 0.9907 1.0008 0.994 1.00371.0767 1.159 1.2426 1.3635 1.5026 1.7162 1.9703 2.2183 2.4312 u21 0.84050.9921 0.9983 0.9931 1.0041 1.0855 1.1625 1.2422 1.3635 1.5002 1.71481.9699 2.2184 2.4316 u22 0.8431 0.9952 0.9965 0.9933 1.0042 1.07171.1524 1.2323 1.3602 1.5018 1.715 1.9702 2.2188 2.4316 u23 0.845 0.99810.995 0.9925 1.0044 1.0641 1.1499 1.2325 1.3599 1.5041 1.7163 1.97042.2189 2.4316 u24 0.8746 0.9923 1.0083 1.0042 1.0029 1.0407 1.09811.1559 1.3074 1.4681 1.6823 1.9579 2.2343 2.4767 u25 0.8744 0.9931 1.0071.0033 1.0027 1.0489 1.1008 1.1557 1.3067 1.4656 1.6809 1.9576 2.23432.4771 u26 0.873 0.9933 1.0054 1.0016 1.0022 1.063 1.1107 1.1651 1.3091.4637 1.6806 1.9574 2.234 2.4776 u27 0.8741 0.994 1.0044 1.0011 1.00181.0547 1.1075 1.166 1.3077 1.4659 1.6819 1.9577 2.2339 2.4776 u28 0.88170.9961 1.0075 1.0052 1.0014 1.0346 1.0666 1.1419 1.2759 1.4395 1.67541.957 2.2354 2.4777 u29 0.8814 0.9967 1.0066 1.004 1 1.0428 1.06861.1419 1.2744 1.437 1.6741 1.9567 2.2355 2.478 u30 0.8834 0.9971 1.00641.0048 1 1.0285 1.058 1.1338 1.2704 1.4386 1.6743 1.957 2.2358 2.478 u310.8841 0.9972 1.006 1.0043 0.9994 1.0201 1.0547 1.1348 1.2687 1.44071.6756 1.9574 2.2358 2.4781 u32 1.3629 2.0409 2.4229 2.7785 3.02863.5525 3.452 3.2399 3.2723 3.4148 3.6596 3.9456 4.2195 4.455 u33 1.36162.0404 2.4238 2.7775 3.0179 3.3285 3.4601 3.2664 3.272 3.4212 3.65973.9438 4.2175 4.4543 u34 1.358 2.0382 2.4229 2.7662 2.9906 3.05 3.39843.2771 3.3022 3.4405 3.6743 3.9524 4.2191 4.4538 u35 1.3599 2.03822.4261 2.7681 2.9999 3.1665 3.3893 3.2497 3.3014 3.4349 3.6736 3.95354.2197 4.4544 u36 1.345 2.0329 2.4052 2.7142 2.9046 2.8657 3.0974 3.23933.3361 3.4975 3.7337 4.0015 4.2519 4.4678 u37 1.3438 2.0323 2.4051 2.7132.8958 2.8059 3.1063 3.2614 3.3361 3.5053 3.7343 4.0001 4.2499 4.4671u38 1.3479 2.0341 2.4101 2.7237 2.9186 2.9411 3.128 3.2458 3.3058 3.48563.7178 3.9905 4.2468 4.4675 u39 1.3497 2.034 2.4127 2.7252 2.9269 3.02363.1188 3.2208 3.3054 3.4793 3.7171 3.9919 4.2479 4.4682 u40 1.28262.0133 2.365 2.5997 2.6751 2.8004 2.9034 3.0715 3.3102 3.5467 3.87764.2522 4.6189 4.9499 u41 1.2818 2.0123 2.3637 2.5981 2.6701 2.74922.9078 3.0856 3.3109 3.554 3.8792 4.251 4.6171 4.9486 u42 1.2788 2.00972.3605 2.5883 2.6558 2.656 2.8982 3.0946 3.3356 3.5759 3.8991 4.26514.622 4.9478 u43 1.2804 2.0091 2.362 2.589 2.6631 2.6836 2.8851 3.07833.3366 3.5679 3.8974 4.2665 4.6241 4.9489 u44 1.2944 2.014 2.3852 2.63292.7231 2.8828 3.0342 3.0854 3.3064 3.5069 3.8306 4.204 4.5744 4.9257 u451.2935 2.0131 2.384 2.6311 2.7177 2.8219 3.0433 3.1019 3.3071 3.51373.8318 4.2028 4.5726 4.9245 u46 1.2972 2.0149 2.3879 2.6404 2.73542.9691 3.0594 3.0876 3.2821 3.4927 3.8137 4.1902 4.5683 4.9251 u47 1.2992.0145 2.3898 2.6411 2.7422 3.0569 3.0508 3.0704 3.282 3.4857 3.81254.1918 4.5703 4.9262 u48 1.5313 2.0191 2.3561 2.6229 2.8594 3.58883.5261 3.7149 4.3926 4.8997 5.2665 5.7826 6.2706 6.6945 u49 1.52912.0206 2.3598 2.6233 2.8526 3.3576 3.5326 3.7612 4.3914 4.9813 5.31235.8072 6.2826 6.6978 u50 1.5241 2.0213 2.3599 2.6144 2.8323 3.07283.4598 3.7455 4.4316 5.0823 5.3952 5.8874 6.3481 6.7426 u51 1.52562.0228 2.3654 2.6171 2.8413 3.1848 3.4525 3.706 4.4301 4.9982 5.34355.8583 6.3349 6.7394 u52 1.507 2.0211 2.3471 2.5738 2.7683 2.8691 3.13053.6125 4.2759 4.7815 5.3532 5.9582 6.5204 7.0147 u53 1.5051 2.02262.3509 2.5745 2.7619 2.8099 3.1398 3.6443 4.2761 4.8302 5.3948 5.9886.5386 7.022 u54 1.5094 2.0257 2.3572 2.5845 2.7819 2.9556 3.1622 3.64884.2348 4.7643 5.327 5.9103 6.4612 6.9572 u55 1.511 2.0274 2.3625 2.58722.7902 3.0453 3.1527 3.6138 4.234 4.7176 5.2885 5.8843 6.4457 6.9515 u561.6021 2.0284 2.3939 2.7143 3.1057 3.5076 3.689 4.5134 4.8429 5.12356.0822 6.8988 7.6405 8.2935 u57 1.5995 2.0305 2.3955 2.7123 3.09293.3048 3.6869 4.5115 4.842 5.2273 6.214 7.0241 7.7438 8.3667 u58 1.59412.031 2.3942 2.7005 3.0605 3.0374 3.5882 4.3291 4.8102 5.309 6.24587.0937 7.8834 8.5802 u59 1.5954 2.0347 2.3975 2.7015 3.0727 3.14573.5857 4.3044 4.8112 5.2174 6.1432 6.9892 7.7827 8.4912 u60 1.61452.0398 2.417 2.7561 3.212 3.8643 4.617 4.9699 5.625 6.2727 6.9795 7.81268.6889 9.531 u61 1.6118 2.0429 2.417 2.7528 3.1958 3.5371 4.4599 4.90355.6215 6.2593 7.0494 7.9583 8.8773 9.7608 u62 1.6162 2.0472 2.42112.7624 3.2323 4.2147 5.1263 5.6564 6.9712 7.0092 7.8747 8.854 9.82410.7896 u63 1.6177 2.0493 2.4237 2.7617 3.244 5.598 6.2209 6.8304 6.98638.3585 9.343 10.4137 11.462 12.4776 SNR 14 15 16 17 18 19 20 21 22 23 2425 26 27 u1 0.9999 0.9999 1 1.0001 0.9997 0.9998 1.0001 0.9997 1.00051.0006 1.0001 1.001 1.0002 0.9999 u2 0.9999 1 1.0003 1.0003 0.99960.9995 0.9999 1.0002 0.9999 1.0007 1.0001 1 1.0001 1.0007 u3 0.99980.9998 1.0002 1.0003 0.9994 0.9993 0.9999 0.9999 1.0004 1.0009 1.00071.0014 1.0007 0.999 u4 0.9996 0.9978 0.9975 0.9985 0.9999 1.0003 0.99991.0004 1.0014 1.0275 1.3247 1.8719 2.2327 2.4633 u5 0.9996 0.9977 0.99740.9986 0.9997 1.0001 1.0002 0.9996 1.0019 1.0279 1.3238 1.8728 2.23362.4642 u6 0.9994 0.9974 0.9971 0.9984 0.9995 0.9999 0.9997 1.0005 1.00151.0275 1.3243 1.8711 2.2327 2.4657 u7 0.9994 0.9972 0.997 0.9984 0.99930.9996 1 1 1.002 1.0279 1.3238 1.8723 2.2333 2.4652 u8 0.9951 1.01191.0641 1.2256 1.6094 2.0167 2.3187 2.5221 2.6542 2.7457 3.0728 3.67974.0893 4.358 u9 0.9952 1.0118 1.0641 1.2257 1.6092 2.0163 2.3185 2.52212.6545 2.7465 3.0724 3.6786 4.0902 4.3579 u10 0.9953 1.0119 1.06431.2259 1.6091 2.0163 2.3187 2.5218 2.6545 2.7465 3.0727 3.6794 4.09064.3587 u11 0.9952 1.0117 1.0642 1.2259 1.6089 2.016 2.3188 2.522 2.65462.7466 3.0727 3.6793 4.0898 4.3588 u12 0.9945 1.0132 1.0667 1.22741.6105 2.0168 2.3179 2.5218 2.6643 2.8236 3.5071 4.6309 5.3838 5.8735u13 0.9946 1.0131 1.0667 1.2275 1.6103 2.0166 2.3178 2.5218 2.66482.8242 3.5073 4.6315 5.3844 5.8717 u14 0.9944 1.0128 1.0664 1.22731.6101 2.0164 2.3178 2.5221 2.664 2.8237 3.5056 4.6308 5.3849 5.8724 u150.9943 1.0126 1.0663 1.2273 1.6098 2.0159 2.3178 2.5224 2.6648 2.82343.507 4.6313 5.3852 5.872 u16 2.5761 2.6771 2.7747 2.9747 3.4295 3.90684.259 4.4941 4.631 4.7146 5.3762 6.5959 7.3934 7.901 u17 2.5759 2.67692.7747 2.9748 3.4293 3.9071 4.2591 4.4942 4.6316 4.7147 5.3781 6.59557.3896 7.9034 u18 2.5761 2.6766 2.7745 2.9749 3.4291 3.9064 4.25914.4944 4.632 4.7157 5.376 6.5969 7.3914 7.9033 u19 2.5758 2.6765 2.77442.9748 3.4289 3.9064 4.259 4.4945 4.6321 4.7156 5.3768 6.5951 7.39147.9016 u20 2.5757 2.6807 2.7808 2.9792 3.4318 3.9075 4.2591 4.50354.6889 4.9481 6.0434 7.7141 8.8142 9.5277 u21 2.5756 2.6805 2.78082.9793 3.4316 3.9074 4.2594 4.5036 4.689 4.9489 6.0427 7.7138 8.81459.5234 u22 2.5753 2.6804 2.7809 2.9792 3.4314 3.9067 4.2591 4.50374.6881 4.9482 6.0423 7.7129 8.8163 9.5246 u23 2.5751 2.6803 2.78082.9792 3.4313 3.907 4.2598 4.5039 4.6882 4.9477 6.0431 7.7148 8.81389.5258 u24 2.6708 2.8589 3.0989 3.5599 4.4098 5.2362 5.8285 6.20896.4094 6.5755 7.7134 9.5764 10.7824 11.5512 u25 2.6707 2.8587 3.09893.56 4.4097 5.2356 5.8281 6.2088 6.4093 6.5743 7.7142 9.5751 10.782811.5554 u26 2.6706 2.8584 3.0987 3.5601 4.4096 5.2357 5.8291 6.20876.4093 6.5769 7.7139 9.5761 10.7815 11.5581 u27 2.6704 2.8584 3.09863.56 4.4093 5.2354 5.8289 6.2089 6.4094 6.5748 7.7127 9.575 10.783311.553 u28 2.6696 2.8533 3.0899 3.5516 4.4062 5.2382 5.8505 6.29046.6495 7.1289 8.692 10.9478 12.4191 13.3731 u29 2.6694 2.8531 3.08993.5517 4.4061 5.2378 5.8507 6.2908 6.6497 7.1297 8.6912 10.9479 12.419513.3502 u30 2.6689 2.8531 3.0901 3.5517 4.4059 5.238 5.8508 6.29066.6488 7.1283 8.6933 10.9474 12.4173 13.3487 u31 2.6686 2.8531 3.09013.5517 4.4054 5.2375 5.8508 6.2913 6.649 7.1282 8.6913 10.9473 12.419213.3722 u32 4.6187 4.7607 4.9645 5.4476 6.4234 7.3577 7.984 8.35118.5574 8.8785 10.5402 13.0392 14.617 15.5648 u33 4.6188 4.7609 4.96475.4476 6.4234 7.3577 7.9838 8.3502 8.555 8.8796 10.5413 13.0406 14.618415.6646 u34 4.6184 4.7616 4.9658 5.4485 6.4234 7.3577 7.984 8.35078.5578 8.8816 10.5404 13.0391 14.6312 15.6624 u35 4.6185 4.7612 4.96565.4485 6.4232 7.3572 7.9842 8.3515 8.5563 8.8807 10.5401 13.0401 14.631915.5607 u36 4.6124 4.7447 4.9489 5.4402 6.4384 7.4182 8.1423 8.69869.2012 9.8304 11.8335 14.6892 16.4785 17.8395 u37 4.6127 4.745 4.94915.4403 6.4383 7.4183 8.1423 8.6985 9.2003 9.8301 11.8338 14.6915 16.477917.5206 u38 4.6133 4.7442 4.948 5.4394 6.4378 7.4179 8.1433 8.69789.1987 9.829 11.8352 14.7102 16.5702 17.5149 u39 4.6134 4.7438 4.94785.4394 6.4375 7.4173 8.1427 8.6971 9.1986 9.8298 11.8374 14.7102 16.571117.8348 u40 5.2325 5.5363 5.94 6.6655 7.9474 9.1302 9.9272 10.459910.8897 11.4804 13.678 16.8135 18.7036 19.8248 u41 5.2324 5.5368 5.946.6657 7.9469 9.1296 9.927 10.4602 10.8893 11.4791 13.677 16.813218.7045 20.5433 u42 5.2307 5.5377 5.9424 6.6722 7.9544 9.1366 9.930310.4585 10.8877 11.4835 13.7102 16.9334 19.0442 20.5387 u43 5.2302 5.5375.9423 6.6721 7.9545 9.1368 9.9305 10.4598 10.8879 11.4845 13.709916.9333 19.0433 19.8224 u44 5.2392 5.5887 6.0408 6.8364 8.2261 9.57110.6064 11.4263 12.1002 12.8576 15.3198 18.7743 20.9002 23.5006 u455.2391 5.5892 6.0408 6.8366 8.2254 9.5701 10.6058 11.4262 12.099 12.857215.319 18.7761 20.8992 22.3178 u46 5.2404 5.5882 6.0382 6.8289 8.21489.5584 10.5981 11.429 12.1242 12.9343 15.5198 19.2368 21.7361 22.32 u475.24 5.5876 6.0381 6.8288 8.2149 9.5584 10.5982 11.4285 12.1239 12.934415.5203 19.2389 21.7386 23.5021 u48 7.013 7.3345 7.7637 8.6099 10.1711.6313 12.6654 13.4186 14.012 14.7276 17.4193 21.3014 23.7907 25.5077u49 7.0128 7.3333 7.7635 8.6113 10.1716 11.6321 12.6649 13.4183 14.011814.7294 17.4205 21.3024 23.7908 27.071 u50 7.0349 7.3345 7.7495 8.587210.1465 11.6186 12.6808 13.4891 14.1858 15.0687 18.0525 22.3301 25.147627.1051 u51 7.035 7.3356 7.7497 8.5859 10.1447 11.6171 12.6806 13.489914.1851 15.0665 18.051 22.3288 25.1536 25.5048 u52 7.4046 7.8017 8.33369.3452 11.1551 12.8729 14.1217 15.0367 15.7471 16.616 19.7548 24.257127.1695 31.6586 u53 7.4058 7.7994 8.3323 9.3489 11.1624 12.8834 14.131715.0426 15.7489 16.6159 19.7531 24.2712 27.2292 29.1086 u54 7.36337.7915 8.3632 9.4306 11.3056 13.1108 14.4682 15.5375 16.4637 17.568821.022 25.8837 28.9904 29.2925 u55 7.3624 7.7933 8.3644 9.4269 11.297113.0972 14.4521 15.5234 16.4628 17.5857 21.0793 26.0304 29.3208 31.0453u56 8.8065 9.3135 9.9376 11.0884 13.1378 15.0593 16.4427 17.4752 18.320919.3541 22.9699 28.108 31.3876 34.8066 u57 8.8474 9.3315 9.9371 11.071413.1081 15.0256 16.4193 17.4806 18.3726 19.4911 23.263 28.6693 32.290936.6067 u58 9.1327 9.6836 10.3651 11.612 13.8329 15.9587 17.5435 18.759819.746 20.9135 24.8649 30.5061 34.1994 38.3565 u59 9.0672 9.6447 10.358311.6469 13.92 16.1127 17.7783 19.0856 20.2014 21.5612 25.8244 31.857235.8395 33.6374 u60 10.241 10.929 11.7451 13.1656 15.6366 17.955619.6557 20.9527 22.03 23.3514 27.7978 34.122 38.2463 41.6053 u61 10.499411.228 12.0958 13.598 16.2181 18.729 20.6497 22.1512 23.4014 24.884629.6552 36.3897 40.7559 43.927 u62 11.6406 12.4845 13.4986 15.198318.1005 20.8322 22.8713 24.4239 25.6952 27.2098 32.2996 39.4812 44.064747.2753 u63 13.3608 14.2674 15.3815 17.2797 20.5285 23.5625 25.793827.4371 28.746 30.303 35.8031 43.5599 48.394 51.6747 SNR 28 29 30 u1 10.9941 1.0006 u2 0.9961 0.9992 1.213 u3 0.9985 1.0038 1.21 u4 2.61172.7108 2.9641 u5 2.6119 2.7122 2.9636 u6 2.6108 2.7177 3.2056 u7 2.60922.7167 3.2068 u8 4.5274 4.6511 5.1068 u9 4.5254 4.6491 5.1065 u10 4.52584.6621 5.4289 u11 4.5276 4.6634 5.4289 u12 6.1814 6.3913 7.1006 u136.1801 6.3942 7.0992 u14 6.1819 6.4253 7.5493 u15 6.181 6.4219 7.5507u16 8.2092 8.414 9.3721 u17 8.2092 8.4115 9.3723 u18 8.2196 8.493 9.9573u19 8.2196 8.4937 9.9568 u20 9.9591 10.2022 11.5446 u21 9.9545 10.200811.5437 u22 9.9731 10.3908 12.2584 u23 9.978 10.392 12.2575 u24 11.992912.2139 13.97 u25 11.9987 12.2143 13.9706 u26 12.0585 12.6031 14.8316u27 12.0523 12.6008 14.8311 u28 13.85 14.1771 16.4155 u29 13.846114.1776 16.4152 u30 14.0343 14.8201 17.4439 u31 14.0384 14.8185 17.4452u32 16.0188 16.526 19.1973 u33 16.0226 16.5255 19.1981 u34 16.462717.3853 20.3747 u35 16.4617 17.3844 20.3735 u36 18.1241 18.9258 22.0463u37 18.1257 18.9254 22.0474 u38 18.8767 19.9861 23.3893 u39 18.881219.9855 23.3882 u40 20.6662 21.6869 25.2366 u41 20.6656 21.6863 25.2361u42 21.7376 22.959 26.7625 u43 21.7386 22.9576 26.7689 u44 23.457624.6756 28.6507 u45 23.4597 24.6791 28.6958 u46 24.8544 26.1926 30.3706u47 24.8569 26.2204 30.5402 u48 26.8146 28.1094 32.437 u49 26.839428.2358 32.8644 u50 28.4818 29.8243 34.4657 u51 28.6146 30.1978 35.2449u52 30.4923 31.9052 36.9762 u53 30.9361 32.6793 38.1036 u54 32.592734.2525 39.8085 u55 33.5509 35.447 41.281 u56 35.418 37.2676 43.2674 u5736.8325 38.8242 45.0812 u58 38.7904 40.803 47.2854 u59 40.7347 42.824849.5626 u60 43.2185 45.313 52.3141 u61 45.8981 48.0239 55.3102 u6249.2922 51.3988 59.013 u63 53.675 55.7554 63.7521g) 65536-QAM/256-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9999 0.9999 0.9999 0.99981.0006 0.9987 1.0011 1.0061 1.0106 1.0072 0.995 1.0017 1.0001 1.0007 u20.9999 0.9992 0.999 0.9992 1.0011 0.9977 1.0019 1.0397 0.9828 0.98870.9887 0.9974 1.0003 1.002 u3 0.9999 0.9995 0.9985 0.9989 1.0021 0.99681.0029 1.0368 0.9737 0.9812 0.9945 0.9951 1.0003 1.0014 u4 0.9995 0.99680.9959 0.9973 1.0025 0.9958 1.0028 1.0735 1.0355 0.9466 0.9768 0.98740.9983 1.0022 u5 0.9994 0.9967 0.9957 0.9971 1.0032 0.9952 1.003 1.07831.0464 0.953 0.972 0.9891 0.9984 1.0029 u6 0.9994 0.9975 0.9962 0.99711.0038 0.9945 1.0036 1.0457 1.0772 0.9704 0.9798 0.9925 0.9984 1.0017 u70.9995 0.9978 0.9958 0.9968 1.0047 0.9934 1.0039 1.0406 1.0667 0.96280.9858 0.9903 0.9983 1.0012 u8 0.9987 0.9858 0.9859 0.9897 1.0036 0.9921.0017 1.0742 1.1355 1.0509 0.9696 0.9935 0.9849 0.9958 u9 0.9987 0.98570.9858 0.9894 1.0045 0.9913 1.0016 1.0791 1.1472 1.0587 0.9647 0.99520.9849 0.9965 u10 0.9986 0.985 0.985 0.9889 1.0049 0.9907 1.0014 1.11291.1145 1.0389 0.9585 0.991 0.9848 0.9978 u11 0.9986 0.9853 0.9845 0.98871.0057 0.9903 1.0015 1.1076 1.103 1.0312 0.9638 0.9888 0.9847 0.9973 u120.999 0.9882 0.9866 0.9897 1.0068 0.9896 1.0019 1.0674 1.0358 1.06970.9823 0.9958 0.9867 0.9966 u13 0.9989 0.9881 0.9865 0.9895 1.00720.9892 1.0015 1.0723 1.0465 1.0778 0.9773 0.9977 0.9867 0.9973 u14 0.9990.9889 0.9871 0.9896 1.0081 0.9885 1.0015 1.0395 1.077 1.0982 0.98471.0016 0.9866 0.9962 u15 0.999 0.9892 0.9866 0.9893 1.0086 0.9877 1.00141.0342 1.066 1.09 0.9902 0.9995 0.9865 0.9956 u16 0.995 0.9494 0.94470.9568 0.9971 0.9929 0.9987 1.0732 1.1387 1.2263 1.1006 1.0039 0.97510.9687 u17 0.995 0.9493 0.9447 0.9567 0.9973 0.9926 0.9983 1.0784 1.15041.2352 1.0939 1.006 0.9752 0.9694 u18 0.9949 0.9487 0.9438 0.9563 0.99760.9924 0.9979 1.1121 1.118 1.2125 1.0854 1.0018 0.9753 0.9706 u19 0.9950.949 0.9435 0.9561 0.998 0.9922 0.9978 1.1072 1.1066 1.2033 1.09150.9998 0.9752 0.9701 u20 0.9946 0.9465 0.9411 0.9548 0.9978 0.99180.9972 1.1489 1.179 1.1598 1.0703 0.9922 0.9736 0.9708 u21 0.9945 0.94650.9411 0.9547 0.9982 0.9916 0.9972 1.1543 1.1911 1.1686 1.064 0.99420.9737 0.9716 u22 0.9945 0.9473 0.9415 0.9548 0.9985 0.9913 0.99741.1196 1.2251 1.1908 1.072 0.9981 0.9734 0.9705 u23 0.9946 0.9476 0.94120.9547 0.9989 0.9912 0.9977 1.1146 1.213 1.1819 1.0782 0.9962 0.97330.9701 u24 0.9954 0.9588 0.9498 0.9608 1.0009 0.9914 0.9981 1.07641.1374 1.0787 1.0934 0.9942 0.9849 0.9756 u25 0.9953 0.9588 0.94970.9606 1.0012 0.9912 0.9985 1.0815 1.1491 1.087 1.0873 0.9962 0.9850.9763 u26 0.9953 0.9581 0.949 0.9602 1.0014 0.9909 0.9988 1.1154 1.11651.0667 1.0794 0.9921 0.9851 0.9776 u27 0.9953 0.9584 0.9486 0.96021.0017 0.9905 0.9998 1.1102 1.105 1.0589 1.0858 0.9902 0.9851 0.9771 u280.9957 0.9611 0.9507 0.9612 1.0026 0.9902 1.0011 1.0702 1.0378 1.09881.1065 0.9984 0.9872 0.9765 u29 0.9957 0.961 0.9507 0.9611 1.003 0.98981.0021 1.0753 1.0486 1.1074 1.1007 1.0005 0.9873 0.9773 u30 0.99570.9618 0.9511 0.9612 1.0033 0.9894 1.0037 1.0427 1.0792 1.1286 1.10911.0047 0.9873 0.9763 u31 0.9958 0.962 0.9509 0.9611 1.0037 0.989 1.00471.0379 1.0683 1.1208 1.1161 1.0027 0.9873 0.9758 u32 0.9988 0.85940.8156 0.8501 1.0099 0.9903 0.9902 1.0718 1.1384 1.2695 1.5234 1.8242.2152 2.5559 u33 0.9985 0.8605 0.8161 0.8507 1.0092 0.9905 0.99221.0764 1.1499 1.279 1.5153 1.8294 2.2133 2.5567 u34 0.9983 0.8605 0.81610.8509 1.0083 0.9905 0.993 1.1098 1.1171 1.2566 1.5053 1.8192 2.21072.5577 u35 0.9982 0.8619 0.8163 0.8515 1.0075 0.991 0.9949 1.1041 1.10531.2477 1.5134 1.8139 2.2123 2.5568 u36 0.9976 0.8606 0.815 0.8507 1.00660.9907 0.9959 1.1455 1.1776 1.204 1.4899 1.7992 2.2032 2.5552 u37 0.99740.8613 0.8154 0.8513 1.0058 0.991 0.9977 1.1501 1.1893 1.2133 1.48171.8044 2.2015 2.556 u38 0.9973 0.8629 0.8165 0.8521 1.005 0.9916 0.99851.1145 1.223 1.2361 1.4919 1.8145 2.2039 2.5549 u39 0.9972 0.8643 0.81670.8524 1.0041 0.992 0.9995 1.1088 1.2107 1.2273 1.5002 1.8092 2.20552.554 u40 0.9961 0.8555 0.8101 0.8477 1.0028 0.9899 1.0007 1.1477 1.28991.3449 1.4919 1.8323 2.2051 2.5426 u41 0.9959 0.8565 0.8109 0.848 1.00180.9902 1.0021 1.152 1.302 1.3544 1.4835 1.8378 2.2032 2.5434 u42 0.99560.8573 0.8107 0.8483 1.0009 0.9905 1.0026 1.1869 1.2672 1.3311 1.4731.8272 2.2006 2.5444 u43 0.9955 0.8585 0.8111 0.8489 0.9999 0.99121.0032 1.181 1.2547 1.3217 1.4813 1.8216 2.2024 2.5435 u44 0.9958 0.86160.8132 0.8502 0.9993 0.9919 1.0037 1.1382 1.1777 1.3674 1.5058 1.83712.2118 2.5449 u45 0.9955 0.8627 0.8139 0.8509 0.9986 0.9925 1.00441.1428 1.1895 1.3769 1.4974 1.8426 2.2099 2.5458 u46 0.9955 0.86380.8149 0.8515 0.9979 0.9931 1.0047 1.1081 1.2233 1.4 1.5078 1.85332.2127 2.5446 u47 0.9954 0.865 0.8152 0.8519 0.997 0.9937 1.0048 1.10251.211 1.3909 1.5163 1.8476 2.2146 2.5437 u48 1.0009 0.8931 0.8438 0.87631.0045 0.9965 0.9947 1.0691 1.1358 1.2388 1.353 1.8195 2.216 2.57 u491.0007 0.8933 0.844 0.8765 1.0042 0.9965 0.9954 1.074 1.1473 1.2481.3454 1.8248 2.2141 2.5709 u50 1.0006 0.8933 0.8436 0.8765 1.00390.9966 0.9957 1.1076 1.1147 1.2255 1.3359 1.8148 2.2113 2.5719 u511.0006 0.894 0.8436 0.8766 1.0037 0.9968 0.9963 1.1023 1.1033 1.21651.3437 1.8096 2.213 2.5712 u52 1.0001 0.8923 0.842 0.8758 1.0029 0.99670.9965 1.1435 1.1753 1.1728 1.3205 1.7949 2.2038 2.5697 u53 0.99990.8927 0.8422 0.876 1.0026 0.9968 0.9971 1.1485 1.1872 1.1818 1.3131.8001 2.2019 2.5706 u54 0.9999 0.8938 0.8428 0.8763 1.0025 0.997 0.99731.1136 1.2211 1.2042 1.3228 1.81 2.2044 2.5697 u55 0.9999 0.8944 0.84280.8764 1.0024 0.9971 0.9977 1.1084 1.209 1.1952 1.3306 1.8047 2.20612.5689 u56 1.0008 0.9041 0.85 0.8816 1.0045 0.9982 0.9992 1.0715 1.13361.0908 1.3414 1.783 2.2071 2.5793 u57 1.0007 0.9044 0.8501 0.8817 1.00430.9982 0.9995 1.0766 1.1453 1.0989 1.3339 1.7882 2.2051 2.5802 u581.0006 0.9043 0.8497 0.8816 1.0041 0.9983 0.9998 1.1103 1.1127 1.07831.3244 1.7789 2.2021 2.5812 u59 1.0006 0.9048 0.8496 0.8816 1.00410.9983 1.0004 1.1051 1.1013 1.0701 1.3319 1.7741 2.2033 2.5805 u60 1.0010.9073 0.8513 0.8826 1.0047 0.9984 1.0011 1.0662 1.0346 1.1103 1.35491.7883 2.2119 2.5822 u61 1.0009 0.9075 0.8515 0.8827 1.0046 0.99831.0015 1.0713 1.0453 1.1186 1.3473 1.7935 2.2098 2.5831 u62 1.00090.9083 0.852 0.8829 1.0048 0.9983 1.0018 1.0388 1.0758 1.1395 1.35691.8032 2.2122 2.5822 u63 1.0009 0.9088 0.8518 0.8829 1.0049 0.99831.0025 1.0339 1.0648 1.1309 1.3645 1.7984 2.2138 2.5815 u64 1.00140.8832 1.3023 1.8457 2.8713 3.3468 3.6733 4.694 4.3631 3.9582 3.67683.9502 4.3585 4.6922 u65 1.0014 0.8832 1.3029 1.846 2.8725 3.3462 3.67314.564 4.2294 3.909 3.6877 3.9552 4.3481 4.6869 u66 1.0013 0.8828 1.30191.8455 2.8727 3.3444 3.6729 4.0789 4.6337 4.0402 3.7072 3.9512 4.33284.6741 u67 1.0014 0.8832 1.3019 1.8457 2.8743 3.3445 3.6729 4.14554.8023 4.1009 3.6949 3.9456 4.3415 4.6799 u68 1.001 0.8812 1.2984 1.84272.8709 3.3391 3.6726 3.8727 4.1949 4.4441 3.7838 3.9628 4.327 4.6633 u691.0009 0.8813 1.2989 1.8431 2.8724 3.3383 3.6724 3.8289 4.1122 4.36643.7988 3.9683 4.3171 4.6583 u70 1.001 0.882 1.3002 1.8441 2.8745 3.33963.6725 4.0201 3.9095 4.1929 3.7754 3.9729 4.3316 4.6713 u71 1.00110.8823 1.3002 1.8444 2.8764 3.3397 3.6725 4.081 3.9742 4.2618 3.76133.9676 4.341 4.677 u72 1.0002 0.873 1.2862 1.8278 2.8526 3.3207 3.66913.8523 3.7713 3.9301 3.9063 4.0959 4.5016 4.7241 u73 1.0002 0.873 1.28671.8282 2.8534 3.32 3.6688 3.8097 3.7277 3.8931 3.9258 4.1 4.4915 4.718u74 1.0002 0.8724 1.2859 1.8277 2.8538 3.3184 3.6686 3.6813 3.86383.9879 3.9571 4.098 4.4759 4.7037 u75 1.0003 0.8726 1.2859 1.828 2.85513.3186 3.6687 3.7161 3.9174 4.0289 3.9361 4.0933 4.4861 4.7098 u761.0008 0.8748 1.2899 1.8316 2.861 3.3236 3.6696 3.9052 4.1912 3.8323.8327 4.0706 4.5005 4.7274 u77 1.0008 0.8747 1.2903 1.8318 2.8616 3.3233.6694 3.8574 4.1077 3.7986 3.8494 4.0752 4.4907 4.7214 u78 1.00090.8754 1.2917 1.8329 2.8642 3.3242 3.6695 4.0837 3.9032 3.7217 3.82384.0784 4.506 4.7358 u79 1.0011 0.8755 1.2918 1.8332 2.8656 3.3244 3.66964.1502 3.9697 3.751 3.8086 4.074 4.5159 4.742 u80 0.9959 0.8487 1.22331.7415 2.8108 3.2753 3.6721 3.888 3.7599 3.5872 3.7421 4.1984 4.69015.1385 u81 0.9959 0.8481 1.224 1.742 2.8115 3.2749 3.6714 3.8405 3.71593.561 3.7525 4.2013 4.6807 5.1294 u82 0.996 0.8473 1.2234 1.7417 2.81113.2735 3.6708 3.7045 3.8513 3.6126 3.77 4.2031 4.6667 5.1105 u83 0.99620.8471 1.2235 1.7421 2.8125 3.2739 3.6708 3.7398 3.9043 3.6307 3.7594.2002 4.6762 5.1196 u84 0.996 0.8446 1.2206 1.7395 2.8088 3.269 3.66833.5864 3.7397 3.7667 3.8275 4.2295 4.6693 5.1037 u85 0.9961 0.84421.2213 1.7398 2.8091 3.2686 3.6676 3.565 3.7018 3.7415 3.839 4.23234.6591 5.0946 u86 0.9963 0.8444 1.2226 1.7409 2.8111 3.2699 3.66733.6717 3.609 3.6803 3.8211 4.2315 4.6737 5.1141 u87 0.9965 0.8442 1.22271.7411 2.8119 3.2704 3.6672 3.7095 3.6369 3.7026 3.81 4.2287 4.68355.1234 u88 0.9973 0.8537 1.2359 1.7568 2.8376 3.2884 3.6755 3.84463.7641 3.8355 3.7043 4.1008 4.5056 5.0392 u89 0.9975 0.8532 1.23661.7571 2.8383 3.288 3.6748 3.8013 3.7193 3.8029 3.7141 4.1051 4.49555.031 u90 0.9975 0.8523 1.2361 1.7567 2.8379 3.2867 3.6743 3.666 3.8573.887 3.73 4.1029 4.4797 5.0134 u91 0.9978 0.8521 1.2361 1.7571 2.83893.2871 3.6743 3.7021 3.9102 3.9236 3.7203 4.0984 4.4898 5.0217 u920.9983 0.8541 1.2398 1.7603 2.8444 3.292 3.6759 3.9024 4.1714 3.74933.6567 4.0752 4.5042 5.0381 u93 0.9984 0.8536 1.2403 1.7607 2.84493.2916 3.6753 3.8552 4.0912 3.7198 3.6671 4.0799 4.4944 5.0301 u940.9986 0.854 1.2418 1.7618 2.8469 3.2929 3.6753 4.0694 3.8928 3.65273.6554 4.0831 4.5099 5.0476 u95 0.9988 0.8538 1.2418 1.762 2.8477 3.29333.6754 4.1333 3.9564 3.6776 3.6519 4.0791 4.5199 5.0558 u96 0.9968 0.9371.5256 2.1597 2.8183 3.2753 3.6655 4.5365 4.3213 4.0144 4.3006 6.00296.7863 7.1885 u97 0.9966 0.9372 1.5256 2.1597 2.8189 3.2749 3.66524.4231 4.2037 3.9605 4.3473 5.9087 6.8606 7.1902 u98 0.9965 0.937 1.52392.1586 2.8184 3.2736 3.665 4.0428 4.5739 4.1035 4.4185 6.084 7.01847.2296 u99 0.9965 0.9377 1.5232 2.1584 2.8191 3.2739 3.6658 4.11044.7316 4.1698 4.365 6.2028 6.9192 7.2267 u100 0.996 0.9356 1.5181 2.15392.8151 3.2693 3.6634 3.8459 4.1686 4.53 4.564 6.4135 7.2596 7.4016 u1010.9959 0.9361 1.5181 2.1539 2.8157 3.2689 3.6633 3.7996 4.0887 4.44954.6324 6.3018 7.3731 7.4105 u102 0.9959 0.9372 1.5193 2.1548 2.8173 3.273.6639 3.9715 3.8923 4.2671 4.5453 6.1274 7.1956 7.3518 u103 0.99590.9379 1.5186 2.1546 2.8182 3.2702 3.6647 4.0285 3.955 4.3407 4.48586.2267 7.0986 7.3454 u104 0.995 0.9278 1.5004 2.1329 2.796 3.2537 3.65483.8251 3.7601 3.9671 4.6055 5.8651 6.7617 7.4739 u105 0.9949 0.92811.5006 2.1329 2.7964 3.253 3.6552 3.7825 3.7159 3.9284 4.6553 5.81426.8076 7.4822 u106 0.9948 0.9278 1.4989 2.1319 2.7961 3.2516 3.65563.6586 3.8524 4.027 4.7241 5.9113 6.8926 7.5379 u107 0.9948 0.92851.4984 2.1318 2.7972 3.2517 3.6569 3.6938 3.9054 4.0698 4.67 5.96726.8407 7.5277 u108 0.9952 0.9313 1.5027 2.1359 2.8023 3.256 3.65973.8809 4.1603 3.8661 4.5211 5.8188 6.6438 7.3735 u109 0.9951 0.93171.5029 2.136 2.8026 3.2554 3.6599 3.8358 4.0813 3.8311 4.5721 5.76546.6862 7.3791 u110 0.9951 0.9327 1.5041 2.1369 2.8043 3.2563 3.66094.0319 3.8851 3.7506 4.5073 5.6716 6.6138 7.3362 u111 0.9951 0.93321.5034 2.1368 2.8052 3.2566 3.6618 4.0903 3.9475 3.7811 4.4615 5.71826.576 7.3314 u112 0.9997 0.9705 1.5989 2.2702 2.8515 3.3001 3.67174.5863 4.3526 4.1768 5.5558 6.0707 6.8156 8.305 u113 0.9996 0.97071.5987 2.2698 2.8509 3.3004 3.6703 4.4695 4.227 4.1089 5.734 5.9676.8958 8.3953 u114 0.9995 0.9705 1.5967 2.2686 2.8496 3.2996 3.66924.0468 4.6126 4.2848 5.8955 6.1586 7.0601 8.6764 u115 0.9995 0.97111.5958 2.2682 2.8494 3.3007 3.6689 4.1028 4.7742 4.3662 5.7319 6.28816.9548 8.5465 u116 0.9991 0.9688 1.5906 2.2632 2.8453 3.2964 3.66573.8507 4.1858 4.7273 5.7188 6.4807 7.2954 8.7651 u117 0.999 0.96911.5905 2.2631 2.8447 3.2964 3.6645 3.8095 4.1032 4.6466 5.8238 6.36717.4101 8.8692 u118 0.999 0.9703 1.5913 2.2638 2.8451 3.2983 3.664 3.9953.9005 4.4571 5.7151 6.1874 7.2309 8.6575 u119 0.999 0.9709 1.59052.2635 2.8449 3.2992 3.6638 4.0529 3.9647 4.5402 5.5998 6.2918 7.13128.5697 u120 0.9998 0.9828 1.6085 2.2865 2.863 3.3179 3.6722 4.40614.3635 6.2755 6.5122 7.7183 8.5647 9.5905 u121 0.9996 0.983 1.60832.2862 2.8621 3.3182 3.6707 4.3124 4.2323 6.3107 6.6271 7.5349 8.75989.9065 u122 0.9996 0.9829 1.6063 2.2848 2.8606 3.3174 3.6694 4.01974.622 6.1476 6.6344 7.6321 8.8941 10.0736 u123 0.9996 0.9834 1.60552.2845 2.86 3.3186 3.6688 4.0704 4.7846 6.1519 6.5676 7.7506 8.75529.8558 u124 1 0.9865 1.6099 2.2886 2.862 3.325 3.6688 4.669 6.81896.9881 7.7657 8.6079 10.1845 11.0225 u125 0.9999 0.9868 1.6096 2.28852.8611 3.3252 3.6676 4.4363 7.0127 7.248 7.4229 8.7745 9.9405 11.101u126 0.9999 0.9879 1.6104 2.2891 2.8605 3.3277 3.6665 8.3665 8.66638.8291 7.9912 11.0628 10.6068 12.0247 u127 1 0.9887 1.6096 2.2886 2.85973.3288 3.6654 7.8601 7.9314 7.8682 9.6554 9.4334 12.514 13.9798 SNR 1415 16 17 18 19 20 21 22 23 24 25 26 27 u1 1 1 1 1 1 1 1 1.0001 1 11.0001 1.0002 1.0009 1.0011 u2 1.0005 1 0.9999 0.9999 1 1 1 1.0001 1 11.0003 1.0003 1.001 1.0016 u3 1.0006 1.0001 1 0.9999 1.0001 1 1 1.00020.9999 1 1.0001 1.0002 1.0002 1.0004 u4 1.0019 1.0003 0.9998 1.00031.0018 1.0002 1 1.0002 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7.2895 12.1967 12.866 13.0648 13.050713.1344 13.0661 23.6016 25.5302 u25 6.9212 7.0346 7.0638 7.0418 7.290112.1976 12.8658 13.0659 13.0504 13.1304 13.058 23.5992 25.5124 u266.9214 7.0342 7.0642 7.0405 7.2903 12.1994 12.8636 13.0636 13.054913.1287 13.5872 25.4362 27.5717 u27 6.9214 7.0345 7.0636 7.0405 7.290412.1984 12.8643 13.0642 13.0518 13.1398 13.579 25.4354 27.5781 u286.9224 7.0349 7.0667 7.0972 7.9067 14.0122 14.8618 15.1097 15.105115.1819 15.1752 27.4562 29.681 u29 6.9221 7.0347 7.0672 7.0965 7.90814.0085 14.8599 15.113 15.0992 15.1856 15.1876 27.4558 29.6821 u306.9214 7.0351 7.0671 7.0961 7.9061 14.0092 14.8613 15.1135 15.102315.1927 16.0237 29.3231 31.7549 u31 6.9205 7.0344 7.0668 7.0959 7.905414.0097 14.8597 15.1108 15.1035 15.1814 16.0137 29.3232 31.7594 u328.9908 9.1122 9.1348 9.0707 9.5396 16.0463 16.9244 17.1907 17.171817.2414 17.5113 31.3516 33.8871 u33 8.9911 9.1118 9.1344 9.071 9.539816.0452 16.9259 17.1888 17.1705 17.2417 17.5031 31.353 33.8773 u348.9906 9.1113 9.1351 9.0701 9.539 16.0419 16.9255 17.1882 17.167817.2654 18.5706 33.2528 35.9715 u35 8.991 9.1116 9.1354 9.0705 9.539216.0388 16.9266 17.1881 17.1691 17.2629 18.5644 33.2529 35.9809 u368.9912 9.1123 9.1489 9.2125 10.4775 17.9271 18.9687 19.2795 19.255719.3163 19.9804 35.3025 38.1205 u37 8.9914 9.1122 9.1478 9.2106 10.477817.9298 18.968 19.2804 19.2559 19.3111 19.9788 35.304 38.117 u38 8.99179.1134 9.1472 9.2112 10.4764 17.9299 18.9683 19.2809 19.2553 19.346621.1495 37.2403 40.2362 u39 8.9912 9.1128 9.1476 9.2117 10.4769 17.928518.9672 19.2801 19.2578 19.3621 21.1524 37.2445 40.2239 u40 11.067311.2256 11.2369 11.1059 12.0061 19.9923 21.0777 21.4044 21.3747 21.361722.4953 39.3085 42.3801 u41 11.0668 11.2255 11.2377 11.1066 12.005719.9919 21.0771 21.402 21.3729 21.3876 22.5109 39.3099 42.3847 u4211.067 11.2254 11.237 11.1065 12.0041 19.9952 21.0776 21.4039 21.366321.5155 23.7174 41.2818 44.5501 u43 11.0666 11.225 11.2364 11.104912.0045 19.9964 21.0766 21.4043 21.3679 21.5122 23.7283 41.2832 44.5608u44 11.0657 11.2302 11.2811 11.4342 13.1858 21.9618 23.1874 23.550723.5059 23.4567 25.0719 43.3629 46.7679 u45 11.0671 11.2297 11.281911.435 13.187 21.9641 23.1875 23.5505 23.5042 23.4496 25.0679 43.36546.7714 u46 11.0669 11.2304 11.2825 11.4362 13.1856 21.9643 23.183823.5499 23.5066 23.717 26.3361 45.3749 48.9786 u47 11.0668 11.230111.2812 11.436 13.1857 21.9603 23.187 23.5523 23.5044 23.7238 26.319545.3761 48.9808 u48 13.2397 13.4028 13.3692 13.2007 14.6699 24.071425.3576 25.7368 25.6586 25.5407 27.7266 47.487 51.2241 u49 13.240313.4035 13.3698 13.201 14.6709 24.0717 25.3576 25.7375 25.6592 25.5427.7184 47.4854 51.2195 u50 13.2399 13.4035 13.3701 13.1998 14.670524.0693 25.3565 25.7358 25.6776 26.0607 29.0202 49.5433 53.4655 u5113.2395 13.403 13.3701 13.2006 14.6701 24.0707 25.3553 25.7359 25.674326.0597 29.0174 49.5435 53.4582 u52 13.2404 13.4232 13.5027 13.860715.9969 26.129 27.545 27.9509 27.8297 27.7435 30.4166 51.6853 55.7521u53 13.2416 13.4229 13.5031 13.861 15.9969 26.1272 27.5449 27.952727.8345 27.7437 30.4132 51.6875 55.7264 u54 13.2416 13.4226 13.502813.862 15.998 26.1264 27.5433 27.9522 27.8866 28.6142 31.7338 53.797458.0397 u55 13.2412 13.4229 13.5023 13.8619 15.9969 26.1297 27.544327.9539 27.8863 28.6058 31.7285 53.8007 58.0114 u56 15.4695 15.635415.5294 15.4932 17.4935 28.3018 29.7929 30.2126 30.0253 30.1633 33.142555.9894 60.3628 u57 15.4695 15.6359 15.5294 15.492 17.4932 28.302829.7933 30.2117 30.0251 30.1586 33.1369 55.99 60.3492 u58 15.469815.6351 15.5295 15.4926 17.4933 28.3013 29.7925 30.2145 30.1545 31.292734.5363 58.1615 62.684 u59 15.47 15.6345 15.5299 15.4944 17.4936 28.30229.7914 30.2159 30.1555 31.2986 34.5258 58.1607 62.6805 u60 15.482215.7086 15.8746 16.5486 18.9258 30.4642 32.081 32.5124 32.2268 32.784835.9852 60.3904 65.0661 u61 15.4818 15.7082 15.8741 16.5476 18.926130.465 32.08 32.5102 32.2223 32.7812 35.9871 60.3926 65.0532 u62 15.482215.7077 15.8736 16.5474 18.927 30.4705 32.0774 32.524 32.5194 34.061537.3989 62.6197 67.4533 u63 15.4821 15.7077 15.8741 16.5498 18.926330.4707 32.0782 32.5252 32.525 34.0601 37.4058 62.6194 67.45 u64 17.803917.9235 17.7749 18.0908 20.4681 32.7308 34.4285 34.8508 34.4638 35.538738.8801 64.9059 69.8435 u65 17.8033 17.9229 17.775 18.0916 20.468432.7342 34.4286 34.8517 34.4716 35.5407 38.8762 64.9012 69.8618 u6617.8036 17.9233 17.7746 18.0899 20.4691 32.7353 34.4319 34.8946 35.061136.9021 40.3523 67.197 72.2732 u67 17.8046 17.9235 17.7746 18.09 20.468432.7374 34.4325 34.8942 35.0559 36.8974 40.3446 67.1931 72.2674 u6817.8596 18.1519 18.5207 19.4231 22.0024 35.0307 36.8304 37.2229 36.855138.383 41.8603 69.536 74.7596 u69 17.8589 18.1531 18.5216 19.423322.0024 35.0258 36.832 37.2222 36.8551 38.3841 41.8594 69.5345 74.7295u70 17.8584 18.1533 18.5209 19.4215 22.0014 35.0353 36.8376 37.343437.8414 39.8194 43.3968 71.8934 77.2584 u71 17.8591 18.1523 18.521219.4214 22.0026 35.0373 36.8413 37.3441 37.8414 39.818 43.4039 71.892277.2299 u72 20.2138 20.2778 20.2921 20.9646 23.6204 37.4258 39.297939.6172 39.5116 41.3494 44.9547 74.3042 79.794 u73 20.2143 20.277720.2924 20.9666 23.6212 37.4258 39.2979 39.6173 39.509 41.3364 44.950374.3063 79.7739 u74 20.2146 20.2783 20.2923 20.9653 23.6208 37.435439.3284 39.9222 40.8043 42.8419 46.5098 76.7413 82.3524 u75 20.214420.2769 20.292 20.9651 23.6208 37.432 39.3274 39.9226 40.8082 42.846446.486 76.7436 82.3657 u76 20.42 20.8736 21.5286 22.4713 25.2716 39.889441.819 42.0625 42.4198 44.4117 48.1059 79.225 84.9825 u77 20.419420.8739 21.5305 22.4715 25.2701 39.8807 41.8165 42.0611 42.4209 44.413448.0959 79.2238 84.9999 u78 20.4194 20.8736 21.5298 22.4719 25.271539.8945 41.9135 42.7227 43.8895 45.9884 49.697 81.7531 87.6215 u7920.4195 20.8732 21.5288 22.472 25.2723 39.9024 41.9126 42.7223 43.889745.9742 49.7094 81.7468 87.6724 u80 22.7233 22.8704 23.2313 24.092626.9965 42.4275 44.3814 44.7027 45.527 47.6023 51.3549 84.3422 90.3187u81 22.7236 22.8711 23.2304 24.0923 27.0001 42.4321 44.3853 44.702945.5275 47.601 51.3717 84.3288 90.4311 u82 22.7246 22.8715 23.230224.0924 27.0041 42.4692 44.6426 45.8431 47.1136 49.2392 53.0585 86.980293.0428 u83 22.7242 22.8705 23.2313 24.0935 27.0015 42.461 44.641745.8431 47.103 49.2363 53.0737 86.9711 93.2898 u84 23.3138 24.054124.8112 25.751 28.7832 45.0533 47.0001 47.6949 48.7801 50.9199 54.796889.6586 95.801 u85 23.3127 24.0543 24.8118 25.751 28.7794 45.045 46.998847.696 48.7776 50.9245 54.807 89.6655 96.2763 u86 23.3144 24.054724.8116 25.7552 28.8014 45.1577 47.6181 49.2057 50.4537 52.6302 56.581192.3763 98.6388 u87 23.313 24.0544 24.8109 25.7544 28.8046 45.163847.6189 49.2068 50.4564 52.643 56.5866 92.4194 99.5106 u88 25.504425.9653 26.5789 27.5038 30.6332 47.7278 49.8108 51.0227 52.2038 54.403458.3896 95.1312 101.6507 u89 25.5051 25.9648 26.5791 27.5029 30.635247.725 49.8118 51.0229 52.1989 54.4037 58.3844 95.2633 103.0069 u9025.5053 25.964 26.5809 27.52 30.7141 48.0599 50.9801 52.7432 53.969656.2267 60.2319 97.9117 105.0269 u91 25.5049 25.9644 26.5807 27.52130.7134 48.0654 50.9816 52.7453 53.9632 56.2216 60.2299 98.2343 106.631u92 26.7816 27.6749 28.3939 29.3219 32.5364 50.5027 53.035 54.611355.8117 58.0789 62.0692 100.7297 108.6317 u93 26.7831 27.6761 28.393529.3221 32.5365 50.51 53.0336 54.6119 55.8027 58.0845 62.1495 101.4149110.3993 u94 26.7809 27.6769 28.4103 29.3929 32.7789 51.2992 54.692456.4831 57.7006 59.9745 63.9313 103.7252 112.3836 u95 26.7811 27.677428.4104 29.3936 32.7792 51.2959 54.694 56.4803 57.7011 60.0062 64.1876104.9305 114.3191 u96 28.9133 29.6554 30.3268 31.2106 34.5196 53.586556.7122 58.4546 59.6618 61.925 65.8707 107.0741 116.3731 u97 28.913129.655 30.3276 31.2106 34.5185 53.5784 56.7123 58.4533 59.6589 61.999466.3884 108.7177 118.3829 u98 28.9139 29.6732 30.4037 31.4462 35.108155.0276 58.6598 60.4712 61.6726 63.8904 67.956 110.7913 120.5016 u9928.9145 29.6736 30.403 31.4444 35.1106 55.0302 58.6585 60.4736 61.687864.0956 68.8364 112.6798 122.6396 u100 30.8635 31.7009 32.3378 33.186736.7457 57.2064 60.7699 62.5823 63.7283 65.9028 70.2821 114.777 124.8491u101 30.8637 31.7021 32.3379 33.1877 36.746 57.2057 60.7722 62.590363.8097 66.3942 71.4289 116.8115 127.09 u102 30.8923 31.7987 32.60233.7894 37.832 59.1583 62.9276 64.7595 65.8345 68.061 72.8718 118.9684129.3915 u103 30.8921 31.7987 32.602 33.7912 37.8322 59.1589 62.930564.7912 66.0432 68.9522 74.1587 121.1169 131.7078 u104 33.1103 33.883334.4773 35.4425 39.4064 61.3827 65.2053 67.011 67.9846 70.5191 75.6001123.3634 134.0697 u105 33.1098 33.8828 34.4762 35.442 39.4075 61.388865.2239 67.1249 68.4883 71.7518 77.0182 125.6343 136.4748 u106 33.255934.2269 35.172 36.5807 40.8735 63.6481 67.5701 69.3232 70.2982 73.272478.5537 127.9882 138.9739 u107 33.2568 34.2274 35.1737 36.5807 40.873463.659 67.6342 69.6384 71.2727 74.709 80.0777 130.3969 141.5291 u10835.4684 36.2481 36.9718 38.1902 42.5213 66.0718 70.0278 71.7242 72.970576.2561 81.6684 132.8873 144.1989 u109 35.4689 36.2489 36.9721 38.190142.5275 66.119 70.2374 72.4646 74.349 77.8245 83.2755 135.4437 146.9255u110 35.9949 37.1526 38.3017 39.7394 44.2273 68.5974 72.5659 74.416776.0146 79.477 84.9523 138.085 149.7421 u111 35.9934 37.1496 38.300739.7481 44.2665 68.7677 73.131 75.7125 77.646 81.161 86.7073 140.8074152.6113 u112 38.1816 39.1352 40.0935 41.4613 46.0376 71.2182 75.327177.574 79.3964 82.93 88.4865 143.626 155.5662 u113 38.1774 39.133540.1039 41.516 46.1905 71.7293 76.5081 79.2732 81.1921 84.7563 90.3453146.5311 158.5759 u114 39.4601 40.7841 41.8845 43.2609 47.9278 74.057778.5907 81.1887 83.092 86.6595 92.2971 149.5326 161.6944 u115 39.465440.8108 41.9638 43.4675 48.3853 75.2231 80.3611 83.1387 85.0706 88.644694.3202 152.6251 164.8804 u116 41.6592 42.8235 43.8418 45.1833 50.047177.4591 82.4633 85.2176 87.1495 90.7162 96.3936 155.829 168.1631 u11741.7049 42.9554 44.136 45.7703 51.0365 79.3386 84.5973 87.3964 89.312192.8734 98.5482 159.1453 171.495 u118 43.7517 44.9531 45.9711 47.429352.6487 81.6178 86.9047 89.7118 91.5981 95.1252 100.7916 162.5723174.9686 u119 44.0261 45.4435 46.7742 48.6159 54.1387 83.9545 89.358292.1643 93.9938 97.4803 103.1416 166.1155 178.531 u120 46.1915 47.43748.591 50.2795 55.8617 86.5324 91.9868 94.7707 96.529 99.9355 105.5792169.8029 182.2238 u121 47.0297 48.6433 50.122 51.9653 57.7109 89.294794.8013 97.5359 99.1736 102.4958 108.1276 173.63 186.0831 u122 49.246750.6869 52.0513 53.8713 59.739 92.3002 97.8188 100.4667 101.982 105.1988110.8224 177.6145 190.0792 u123 51.1141 52.7512 54.165 55.9764 61.960395.5521 101.0594 103.5869 104.9459 108.0373 113.5985 181.7798 194.231u124 53.5989 55.1926 56.557 58.314 64.3981 99.1007 104.5481 106.9211108.0924 111.0473 116.55 186.1633 198.5898 u125 56.464 57.9913 59.256360.9174 67.0836 102.97 108.3322 110.5136 111.4395 114.2481 119.6945190.8022 203.2222 u126 59.8456 61.2264 62.3312 63.8479 70.0819 107.2526112.4929 114.4357 115.113 117.7127 123.0838 195.7743 208.1804 u12763.9379 65.0834 65.9472 67.2579 73.5415 112.162 117.228 118.8617119.2181 121.5705 127.0239 201.2647 213.6522h) 262144-QAM/512-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 11 12 13 u1 0.9998 1.0001 0.9999 1 1.00060.9995 0.9998 0.9962 1.0007 0.9963 1.0006 1.0006 1.0001 1.0001 u2 0.99910.9999 0.9995 0.9997 1.001 0.9988 0.9997 0.9948 0.9893 0.9887 0.9960.9998 1.0003 1.0007 u3 0.9986 1 0.9994 0.9995 1.0016 0.9985 0.99960.9944 0.9902 0.9926 0.9952 0.9985 1 1.0007 u4 0.9978 0.9994 0.99860.999 1.0019 0.9979 0.9995 0.9893 0.9616 0.9733 0.9889 0.9943 1.00011.0018 u5 0.9973 0.9995 0.9985 0.9989 1.0022 0.9973 0.9994 0.9847 0.96230.9695 0.9896 0.9947 1.0003 1.0019 u6 0.9968 0.9998 0.9986 0.9989 1.00270.9969 0.9993 0.9818 0.9746 0.9772 0.9941 0.9946 1 1.0014 u7 0.99630.9998 0.9985 0.9987 1.0031 0.9963 0.9993 0.9813 0.9759 0.9811 0.99340.9934 0.9997 1.0015 u8 0.9946 0.9971 0.9963 0.9971 1.0033 0.9958 0.99941.0291 1.0236 0.951 0.976 0.986 0.9983 1.0018 u9 0.9943 0.9972 0.99620.9971 1.0037 0.9954 0.9993 1.0269 1.0243 0.9469 0.9767 0.9864 0.99851.0019 u10 0.9937 0.997 0.9958 0.9968 1.0042 0.995 0.9994 1.027 1.01240.9389 0.9724 0.9855 0.9987 1.0024 u11 0.9932 0.9971 0.9957 0.99671.0046 0.9945 0.9993 1.0276 1.0134 0.9423 0.9718 0.9844 0.9984 1.0025u12 0.993 0.9978 0.9961 0.9969 1.0052 0.994 0.9993 1.0254 1.0456 0.96210.9779 0.9877 0.9981 1.0015 u13 0.9926 0.9978 0.996 0.9968 1.0055 0.99370.9993 1.0234 1.0463 0.958 0.9786 0.9884 0.9983 1.0015 u14 0.992 0.99810.9961 0.9969 1.006 0.9931 0.9992 1.0218 1.0597 0.9656 0.983 0.98840.9981 1.0011 u15 0.9917 0.9982 0.996 0.9966 1.0064 0.9929 0.9993 1.02171.0609 0.9694 0.9825 0.987 0.9978 1.0011 u16 0.9854 0.9856 0.986 0.98941.0047 0.9922 1.0001 1.0799 1.1302 1.0696 0.9687 0.9919 0.9883 0.9939u17 0.9851 0.9857 0.9859 0.9893 1.0052 0.992 1.0001 1.0788 1.13 1.06550.9694 0.9924 0.9887 0.9939 u18 0.9844 0.9855 0.9855 0.9891 1.00550.9915 1.0002 1.0801 1.1161 1.0572 0.9648 0.9918 0.989 0.9944 u19 0.98410.9856 0.9854 0.989 1.006 0.9911 1.0002 1.0822 1.1164 1.0616 0.96420.9906 0.9889 0.9944 u20 0.9832 0.985 0.9847 0.9885 1.0064 0.9907 1.00031.0831 1.082 1.0407 0.9578 0.9869 0.9893 0.9955 u21 0.9826 0.9851 0.98460.9884 1.0066 0.9903 1.0003 1.0824 1.0818 1.0367 0.9585 0.9873 0.98960.9955 u22 0.9823 0.9854 0.9847 0.9884 1.0071 0.9899 1.0003 1.082 1.09541.0455 0.963 0.9873 0.9895 0.995 u23 0.9819 0.9854 0.9845 0.9883 1.00760.9897 1.0004 1.084 1.0957 1.0499 0.9624 0.9862 0.9894 0.995 u24 0.98260.9883 0.9865 0.9895 1.0085 0.9893 1.0002 1.0321 1.043 1.0838 0.98010.9923 0.9908 0.9947 u25 0.9822 0.9884 0.9863 0.9895 1.009 0.9889 1.00031.0311 1.0428 1.0797 0.9807 0.993 0.991 0.9947 u26 0.9818 0.9882 0.98590.9892 1.0093 0.9886 1.0004 1.0323 1.0299 1.0712 0.9762 0.9924 0.99130.9952 u27 0.9811 0.9882 0.9858 0.989 1.0097 0.9884 1.0004 1.0341 1.03011.0757 0.9755 0.9914 0.9911 0.9952 u28 0.9809 0.9889 0.9863 0.98941.0102 0.9879 1.0004 1.033 1.0628 1.0979 0.9817 0.9953 0.9908 0.9942 u290.9804 0.989 0.9861 0.9893 1.0105 0.9876 1.0004 1.0322 1.0626 1.09380.9824 0.9961 0.991 0.9942 u30 0.9801 0.9893 0.9862 0.9892 1.0109 0.98731.0005 1.0313 1.0758 1.1029 0.9868 0.9964 0.9909 0.9937 u31 0.97970.9894 0.9862 0.9891 1.0113 0.987 1.0006 1.0331 1.076 1.1074 0.98610.9954 0.9906 0.9937 u32 0.9865 0.9479 0.9445 0.9566 0.9978 0.99381.0006 1.0721 1.1533 1.2466 1.1002 1.0032 0.978 0.9669 u33 0.9859 0.9480.9444 0.9565 0.998 0.9937 1.0007 1.0709 1.1531 1.2416 1.1011 1.00420.9782 0.9671 u34 0.9856 0.9479 0.9441 0.9564 0.9983 0.9936 1.00081.0722 1.1392 1.2318 1.0958 1.0037 0.9783 0.9678 u35 0.985 0.9479 0.9440.9563 0.9985 0.9935 1.0009 1.0743 1.1395 1.2365 1.0951 1.0028 0.97810.9678 u36 0.9844 0.9474 0.9434 0.9559 0.9987 0.9933 1.001 1.0749 1.10491.2124 1.0878 0.9984 0.9781 0.969 u37 0.9841 0.9475 0.9433 0.9558 0.99880.9931 1.0011 1.0737 1.1047 1.2076 1.0887 0.9994 0.9783 0.9691 u380.9837 0.9477 0.9434 0.9559 0.9991 0.9931 1.0011 1.073 1.1186 1.21731.0941 0.9998 0.9782 0.9686 u39 0.9833 0.9478 0.9434 0.9559 0.9993 0.9931.0012 1.0751 1.1188 1.222 1.0933 0.9989 0.9781 0.9686 u40 0.9818 0.94530.9415 0.9545 0.9991 0.9927 1.0014 1.125 1.1761 1.186 1.0734 0.99130.9756 0.9692 u41 0.9813 0.9454 0.9413 0.9545 0.9993 0.9926 1.00141.1235 1.1759 1.1814 1.0742 0.9922 0.9758 0.9693 u42 0.981 0.9452 0.94110.9543 0.9994 0.9925 1.0015 1.1245 1.1615 1.1717 1.069 0.9919 0.9760.9698 u43 0.9806 0.9453 0.941 0.9542 0.9996 0.9924 1.0015 1.1264 1.16171.1764 1.0682 0.991 0.9758 0.9697 u44 0.9805 0.9459 0.9414 0.9545 10.9922 1.0014 1.126 1.1979 1.2004 1.0754 0.9952 0.9759 0.9685 u45 0.98010.946 0.9413 0.9545 1.0002 0.9921 1.0014 1.1245 1.1977 1.1957 1.07620.9961 0.9761 0.9686 u46 0.9797 0.9462 0.9414 0.9546 1.0004 0.992 1.00141.1237 1.2122 1.2055 1.0814 0.9965 0.9761 0.968 u47 0.9793 0.9463 0.94130.9545 1.0006 0.9918 1.0014 1.1254 1.2124 1.2103 1.0806 0.9956 0.97590.9678 u48 0.9841 0.9581 0.9503 0.9609 1.0031 0.9919 1.0012 1.08131.1302 1.0859 1.0919 0.9951 0.987 0.9726 u49 0.9836 0.9581 0.9502 0.96091.0034 0.9917 1.0012 1.0799 1.1299 1.0817 1.0927 0.996 0.9872 0.9725 u500.9832 0.958 0.9498 0.9607 1.0035 0.9916 1.0011 1.0808 1.1161 1.07331.0873 0.9956 0.9873 0.973 u51 0.9829 0.958 0.9498 0.9606 1.0038 0.99141.0011 1.0823 1.1162 1.0778 1.0864 0.9947 0.9871 0.9729 u52 0.982 0.95750.9492 0.9602 1.0039 0.9911 1.001 1.0826 1.082 1.0566 1.0791 0.99050.9873 0.9739 u53 0.9816 0.9576 0.9491 0.9602 1.0041 0.991 1.001 1.08081.0818 1.0526 1.0798 0.9915 0.9874 0.9738 u54 0.9814 0.9578 0.94920.9602 1.0043 0.9908 1.0009 1.0799 1.0953 1.0616 1.085 0.992 0.98720.9732 u55 0.981 0.9578 0.9492 0.9601 1.0045 0.9906 1.0008 1.0814 1.09551.0662 1.0841 0.9911 0.987 0.9731 u56 0.9816 0.9605 0.9509 0.9613 1.00530.9904 1.0005 1.0319 1.043 1.0994 1.1042 0.9995 0.9881 0.9724 u57 0.98110.9606 0.9508 0.9613 1.0055 0.9902 1.0004 1.03 1.0429 1.0955 1.1051.0005 0.9882 0.9723 u58 0.9806 0.9604 0.9505 0.9612 1.0056 0.99 1.00031.0307 1.0301 1.0873 1.0994 1.0001 0.9884 0.9728 u59 0.9803 0.96040.9505 0.961 1.0059 0.9897 1.0002 1.0317 1.0304 1.092 1.0984 0.99920.9881 0.9726 u60 0.9801 0.9611 0.9509 0.9614 1.0062 0.9895 0.99991.0314 1.0628 1.1143 1.1056 1.0034 0.9878 0.9714 u61 0.9799 0.96120.9508 0.9614 1.0065 0.9893 0.9998 1.0293 1.0627 1.1105 1.1063 1.00440.9879 0.9714 u62 0.9794 0.9614 0.9509 0.9614 1.0068 0.989 0.9996 1.02831.0759 1.12 1.1115 1.0048 0.9876 0.9709 u63 0.979 0.9615 0.9509 0.96131.007 0.9888 0.9994 1.029 1.0761 1.1252 1.1105 1.0039 0.9873 0.9708 u640.9546 0.8578 0.8134 0.8471 1.0124 0.9912 1.0025 1.0806 1.161 1.26561.5203 1.8256 2.2149 2.5504 u65 0.9563 0.8584 0.8137 0.8475 1.01170.9912 1.0023 1.0785 1.1604 1.2606 1.5216 1.8285 2.215 2.5507 u66 0.95720.8587 0.8139 0.8478 1.0113 0.9913 1.002 1.0786 1.146 1.2502 1.51471.827 2.2141 2.5515 u67 0.9585 0.859 0.814 0.8481 1.0109 0.9915 1.00181.0792 1.146 1.2546 1.5134 1.8241 2.2139 2.5512 u68 0.9591 0.8589 0.81390.848 1.0104 0.9915 1.0016 1.0787 1.1109 1.2303 1.5041 1.8141 2.21072.5522 u69 0.9603 0.8595 0.8142 0.8484 1.01 0.9916 1.0013 1.0764 1.11031.2251 1.5054 1.8169 2.2108 2.5525 u70 0.9615 0.86 0.8148 0.8489 1.00950.9917 1.0011 1.0748 1.1239 1.2344 1.5123 1.8183 2.2117 2.5516 u710.9624 0.8606 0.8152 0.8491 1.009 0.9919 1.0009 1.0756 1.1238 1.2391.511 1.8155 2.2115 2.5513 u72 0.9628 0.8587 0.8138 0.8485 1.0085 0.99151.0006 1.1257 1.1816 1.2024 1.4871 1.8008 2.2027 2.5496 u73 0.96370.8591 0.8141 0.8487 1.0081 0.9916 1.0004 1.1238 1.181 1.1973 1.48841.8036 2.2029 2.5498 u74 0.9647 0.8594 0.8143 0.8489 1.0075 0.99181.0002 1.1242 1.1663 1.1874 1.4814 1.8021 2.2019 2.5506 u75 0.9661 0.860.8146 0.8493 1.0072 0.9919 1.0001 1.1254 1.1663 1.1917 1.4802 1.79932.2017 2.5503 u76 0.9672 0.8608 0.8154 0.85 1.0067 0.9922 0.9999 1.12421.2023 1.2154 1.4896 1.8092 2.2048 2.5492 u77 0.9684 0.8613 0.81570.8503 1.0061 0.9923 0.9997 1.1223 1.2018 1.2103 1.4908 1.812 2.2052.5494 u78 0.97 0.8619 0.8162 0.8506 1.0058 0.9925 0.9995 1.121 1.21611.2199 1.4978 1.8135 2.2058 2.5485 u79 0.9709 0.8626 0.8165 0.851 1.00520.9927 0.9994 1.1222 1.2161 1.2243 1.4965 1.8106 2.2056 2.5482 u80 0.9670.853 0.8095 0.8458 1.004 0.9908 0.9993 1.1692 1.302 1.3625 1.48331.8295 2.2012 2.5365 u81 0.9684 0.8535 0.8097 0.8461 1.0037 0.991 0.99921.1674 1.3015 1.3569 1.4847 1.8325 2.2014 2.5367 u82 0.9693 0.85390.8099 0.8463 1.0031 0.9912 0.9991 1.1681 1.2864 1.3461 1.4776 1.8312.2005 2.5375 u83 0.9707 0.8543 0.8104 0.8467 1.0024 0.9914 0.999 1.16951.2865 1.3506 1.4764 1.828 2.2002 2.5372 u84 0.9721 0.8543 0.8102 0.84671.002 0.9915 0.9988 1.1704 1.249 1.3252 1.4668 1.8176 2.1969 2.5383 u850.9728 0.8548 0.8106 0.8471 1.0015 0.9917 0.9987 1.1685 1.2486 1.31961.4681 1.8205 2.1971 2.5385 u86 0.9741 0.8555 0.8112 0.8476 1.00110.9919 0.9986 1.1676 1.2633 1.3294 1.4752 1.822 2.198 2.5376 u87 0.97530.856 0.8114 0.8479 1.0005 0.9922 0.9985 1.1689 1.2634 1.3341 1.4741.819 2.1978 2.5373 u88 0.9772 0.8586 0.8133 0.8492 1.0002 0.9929 0.99841.1157 1.2016 1.3715 1.4985 1.8345 2.2069 2.5389 u89 0.9786 0.859 0.81350.8496 0.9996 0.9931 0.9984 1.1139 1.2012 1.3662 1.4998 1.8375 2.20712.5391 u90 0.9799 0.8594 0.8138 0.8499 0.9991 0.9933 0.9983 1.11461.1864 1.3558 1.4927 1.8359 2.2061 2.5399 u91 0.9808 0.86 0.8141 0.85010.9987 0.9935 0.9982 1.1159 1.1864 1.3605 1.4914 1.8329 2.2059 2.5396u92 0.9819 0.8608 0.8147 0.8507 0.9984 0.9939 0.9982 1.1145 1.22261.3855 1.5009 1.8433 2.2092 2.5384 u93 0.9829 0.8615 0.8151 0.851 0.9980.9942 0.9981 1.1126 1.2223 1.3803 1.5021 1.8463 2.2095 2.5386 u940.9844 0.8619 0.8155 0.8514 0.9973 0.9944 0.9981 1.1116 1.2367 1.39031.5092 1.8478 2.2104 2.5377 u95 0.9854 0.8625 0.8159 0.8518 0.99690.9946 0.998 1.1129 1.2367 1.3952 1.5079 1.8448 2.2102 2.5374 u96 0.96940.8911 0.8434 0.8758 1.0064 0.9966 1.0017 1.0786 1.1574 1.2454 1.34481.8091 2.2111 2.5636 u97 0.9696 0.8915 0.8435 0.8759 1.0063 0.99671.0016 1.0766 1.1571 1.2407 1.3458 1.812 2.2112 2.5638 u98 0.9701 0.89140.8434 0.876 1.0062 0.9967 1.0015 1.077 1.1429 1.231 1.3391 1.81062.2102 2.5645 u99 0.9707 0.8917 0.8435 0.8761 1.006 0.9967 1.0014 1.07841.1431 1.2358 1.3379 1.8078 2.21 2.5642 u100 0.9709 0.8915 0.8432 0.87591.0058 0.9967 1.0013 1.0781 1.1081 1.2119 1.3289 1.7981 2.2065 2.5652u101 0.9714 0.8917 0.8433 0.8761 1.0056 0.9968 1.0012 1.0763 1.10781.2073 1.3299 1.8009 2.2067 2.5654 u102 0.9718 0.8921 0.8435 0.87631.0055 0.9968 1.0012 1.0751 1.1215 1.217 1.3363 1.8023 2.2075 2.5645u103 0.9724 0.8923 0.8437 0.8764 1.0054 0.9969 1.0011 1.0766 1.12161.2219 1.3351 1.7995 2.2072 2.5642 u104 0.9721 0.8904 0.8423 0.87551.0047 0.9968 1.0011 1.126 1.1789 1.1859 1.311 1.7851 2.1982 2.5625 u1050.9726 0.8906 0.8424 0.8757 1.0047 0.9968 1.0011 1.1242 1.1786 1.18121.3119 1.7878 2.1983 2.5627 u106 0.9729 0.8907 0.8423 0.8757 1.00450.9969 1.0011 1.1248 1.1641 1.1717 1.3054 1.7865 2.1973 2.5634 u1070.9735 0.8909 0.8424 0.8758 1.0043 0.9969 1.001 1.1264 1.1642 1.17651.3041 1.7838 2.197 2.5631 u108 0.9739 0.8917 0.8429 0.8762 1.0044 0.9971.0008 1.1258 1.2003 1.2005 1.313 1.7935 2.2002 2.5621 u109 0.97430.8919 0.843 0.8763 1.0043 0.9971 1.0008 1.124 1.2 1.1958 1.314 1.79632.2003 2.5623 u110 0.9748 0.8923 0.8432 0.8764 1.0042 0.9971 1.00071.123 1.2145 1.2057 1.3204 1.7977 2.2011 2.5615 u111 0.9753 0.89240.8433 0.8766 1.0041 0.9972 1.0007 1.1244 1.2146 1.2105 1.3192 1.7952.2007 2.5612 u112 0.9785 0.9026 0.8506 0.8818 1.0069 0.9975 1 1.07881.1336 1.0874 1.3348 1.7774 2.2054 2.5719 u113 0.979 0.9028 0.85060.8819 1.0069 0.9975 1 1.0771 1.1333 1.083 1.3358 1.7802 2.2054 2.5721u114 0.9791 0.9028 0.8505 0.8819 1.0069 0.9975 0.9999 1.0777 1.11941.0743 1.3292 1.7789 2.2043 2.5728 u115 0.9794 0.903 0.8506 0.882 1.00680.9975 0.9998 1.0792 1.1196 1.0785 1.3281 1.7764 2.2039 2.5725 u1160.9797 0.9026 0.8502 0.8817 1.0067 0.9975 0.9998 1.0794 1.0852 1.0571.3192 1.7672 2.2006 2.5733 u117 0.98 0.9029 0.8502 0.8819 1.0066 0.99750.9998 1.0776 1.085 1.0527 1.3202 1.77 2.2007 2.5735 u118 0.9802 0.90320.8504 0.882 1.0067 0.9975 0.9998 1.0766 1.0985 1.0613 1.3266 1.77142.2014 2.5727 u119 0.9805 0.9034 0.8505 0.882 1.0066 0.9975 0.99971.0782 1.0987 1.0653 1.3255 1.7689 2.201 2.5724 u120 0.9812 0.90570.8519 0.883 1.0073 0.9974 0.9995 1.0278 1.0461 1.0986 1.3492 1.78292.2093 2.574 u121 0.9817 0.9059 0.852 0.8831 1.0074 0.9974 0.9994 1.02621.0459 1.0943 1.3502 1.7857 2.2093 2.5742 u122 0.9818 0.9058 0.85180.883 1.0074 0.9974 0.9993 1.0267 1.0331 1.0854 1.3437 1.7844 2.20822.5749 u123 0.982 0.906 0.8519 0.883 1.0073 0.9973 0.9993 1.0282 1.03321.0896 1.3425 1.7819 2.2079 2.5746 u124 0.9823 0.9067 0.8523 0.88331.0075 0.9973 0.9991 1.0282 1.0658 1.1117 1.3513 1.7914 2.2109 2.5736u125 0.9826 0.9068 0.8523 0.8834 1.0076 0.9972 0.9991 1.0265 1.06561.1073 1.3524 1.7942 2.211 2.5738 u126 0.9828 0.9071 0.8524 0.88341.0077 0.9972 0.999 1.0255 1.0788 1.1162 1.3588 1.7956 2.2116 2.573 u1270.9831 0.9073 0.8525 0.8834 1.0077 0.9971 0.9989 1.0271 1.079 1.12061.3577 1.7931 2.2112 2.5727 u128 0.9756 0.8808 1.3017 1.8444 2.87253.3532 3.6746 4.2319 4.1112 3.9432 3.6724 3.9399 4.3558 4.686 u1290.9757 0.8809 1.3017 1.8447 2.8733 3.3528 3.6745 4.2775 4.1131 3.96933.6742 3.9449 4.3544 4.6854 u130 0.9758 0.8809 1.3015 1.8444 2.8743.3524 3.6745 4.2579 4.2341 4.026 3.684 3.9415 4.3493 4.6802 u131 0.97580.8809 1.3016 1.8445 2.8748 3.3523 3.6745 4.22 4.232 3.9977 3.6824 3.9374.3523 4.6794 u132 0.9757 0.8806 1.3008 1.8436 2.8746 3.3508 3.67424.3134 4.6448 4.1662 3.7017 3.9349 4.3357 4.6658 u133 0.9757 0.88071.3009 1.8439 2.8754 3.3506 3.6742 4.3572 4.6481 4.2022 3.7035 3.944.3343 4.6649 u134 0.9757 0.8809 1.3015 1.8444 2.8767 3.3506 3.67434.3836 4.4679 4.1318 3.6933 3.944 4.3414 4.6687 u135 0.9758 0.881 1.30161.8444 2.8776 3.3506 3.6743 4.3461 4.4653 4.0993 3.6917 3.9392 4.34424.6675 u136 0.9752 0.879 1.2986 1.841 2.8735 3.3447 3.6734 3.854 4.12924.4207 3.7812 3.9556 4.3214 4.6541 u137 0.9752 0.8791 1.2987 1.84122.8745 3.3444 3.6734 3.876 4.1308 4.462 3.7826 3.9608 4.3194 4.6534 u1380.975 0.879 1.2985 1.841 2.8752 3.344 3.6733 3.8631 4.2298 4.5456 3.79643.9569 4.3128 4.6483 u139 0.975 0.8791 1.2987 1.8411 2.8761 3.344 3.67333.8404 4.228 4.5024 3.795 3.9516 4.3149 4.6474 u140 0.9751 0.8796 1.29961.8422 2.8781 3.345 3.6736 3.7681 3.9867 4.3011 3.7699 3.9548 4.33254.6596 u141 0.9751 0.8798 1.2998 1.8425 2.8791 3.3448 3.6736 3.78923.988 4.3395 3.7713 3.96 4.3305 4.6591 u142 0.975 0.88 1.3003 1.84292.88 3.3449 3.6736 3.8007 3.9117 4.2646 3.7585 3.9641 4.3372 4.663 u1430.9749 0.8801 1.3004 1.843 2.8812 3.3448 3.6737 3.7784 3.9105 4.22913.757 3.9589 4.3394 4.6621 u144 0.9705 0.8702 1.2859 1.8261 2.85363.3242 3.6705 3.5727 3.7017 3.8676 3.9123 4.0804 4.4853 4.7149 u1450.9703 0.8703 1.2861 1.8264 2.8544 3.3239 3.6704 3.5878 3.7023 3.88443.913 4.0851 4.483 4.715 u146 0.9699 0.8702 1.2859 1.8262 2.8548 3.32353.6703 3.5797 3.7505 3.9198 3.93 4.0812 4.4762 4.7102 u147 0.9697 0.87021.286 1.8263 2.8558 3.3234 3.6704 3.5648 3.7496 3.9015 3.9293 4.07644.4788 4.7102 u148 0.9692 0.8698 1.2853 1.8254 2.8554 3.322 3.67 3.62123.903 4.0007 3.9609 4.0759 4.4619 4.6971 u149 0.9689 0.8698 1.28551.8257 2.8561 3.3217 3.67 3.6367 3.9043 4.0206 3.9614 4.0808 4.45964.6973 u150 0.9687 0.87 1.2859 1.8262 2.8571 3.3218 3.67 3.6452 3.84383.9803 3.9427 4.0847 4.4669 4.7021 u151 0.9684 0.8701 1.2862 1.82622.8578 3.3218 3.67 3.6295 3.8431 3.9605 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3.0083 3.0643 4.6714 4.9178 4.9899 5.0007 5.007 5.0316 10.046710.7509 u23 2.926 2.988 2.9978 3.0087 3.0642 4.6705 4.9171 4.9886 5.00095.0056 5.0337 10.0454 10.7746 u24 2.9261 2.9884 2.998 3.0159 3.20096.3634 6.8446 6.9827 7.0056 7.0188 7.0226 12.0464 12.7787 u25 2.9262.9883 2.998 3.016 3.2012 6.3649 6.8445 6.9821 7.006 7.0162 7.023612.0451 12.7739 u26 2.926 2.9876 2.9977 3.0164 3.2021 6.3652 6.84496.9834 7.0068 7.0172 7.0225 12.046 12.796 u27 2.9261 2.9877 2.99773.0166 3.2017 6.3654 6.8439 6.9832 7.0068 7.0185 7.0221 12.0459 12.7936u28 2.9254 2.9869 2.9972 3.0169 3.2021 6.3656 6.8436 6.9843 7.00667.0174 7.0583 13.7568 14.7454 u29 2.9255 2.9867 2.9972 3.0166 3.20256.3655 6.8436 6.9836 7.0071 7.0171 7.0593 13.755 14.7321 u30 2.92562.9872 2.9977 3.016 3.2019 6.3654 6.8441 6.9831 7.0056 7.0164 7.060613.7554 14.7533 u31 2.9255 2.9873 2.9978 3.0158 3.2012 6.3645 6.84456.9836 7.0053 7.0167 7.0596 13.7551 14.742 u32 4.943 5.0066 5.01385.0267 5.1163 8.3693 8.8596 9.005 9.0251 9.0365 9.0268 15.7582 16.7635u33 4.9428 5.0067 5.0142 5.0261 5.1169 8.3694 8.8581 9.005 9.0227 9.03689.0258 15.7574 16.7563 u34 4.9428 5.0069 5.0143 5.0257 5.1163 8.36948.8589 9.0053 9.0215 9.0349 9.0251 15.7583 16.7781 u35 4.9431 5.00665.0141 5.026 5.1154 8.3699 8.8593 9.0053 9.0232 9.0372 9.0266 15.757816.8022 u36 4.9429 5.0065 5.0143 5.0264 5.1165 8.3701 8.859 9.0057 9.0239.0355 9.1026 17.4856 18.756 u37 4.943 5.0067 5.0146 5.0259 5.11698.3688 8.8579 9.0058 9.0213 9.0357 9.1029 17.4872 18.7621 u38 4.94315.0064 5.0144 5.0263 5.1176 8.3691 8.8581 9.0061 9.0232 9.0361 9.102817.4879 18.7421 u39 4.9431 5.0063 5.0141 5.0265 5.1171 8.3698 8.85899.0058 9.0244 9.0362 9.1028 17.4864 18.7824 u40 4.9434 5.007 5.01465.0464 5.3808 10.1049 10.8109 11.0209 11.0452 11.0631 11.0233 19.490120.7983 u41 4.9431 5.0072 5.0148 5.0458 5.3821 10.1052 10.8111 11.020711.0469 11.0636 11.0241 19.4896 20.8081 u42 4.943 5.0074 5.0147 5.04585.3819 10.1043 10.8111 11.0201 11.0477 11.0623 11.0245 19.4909 20.7991u43 4.9432 5.0072 5.0145 5.0461 5.3807 10.106 10.8102 11.0201 11.045511.062 11.0235 19.4897 20.8173 u44 4.9427 5.0075 5.0136 5.0456 5.379810.1054 10.8103 11.0208 11.0452 11.0615 11.1787 21.2453 22.758 u454.9428 5.0076 5.014 5.0453 5.3808 10.1043 10.8108 11.0209 11.047711.0619 11.1793 21.245 22.7904 u46 4.943 5.0072 5.0141 5.0453 5.381210.1046 10.8112 11.0214 11.0474 11.0617 11.1788 21.244 22.7842 u474.9429 5.0069 5.0139 5.0459 5.38 10.1056 10.811 11.0213 11.0442 11.062911.1783 21.2443 22.7874 u48 6.9184 7.035 7.0489 7.0528 7.18 12.116812.8458 13.0654 13.0877 13.098 13.0171 23.2538 24.7711 u49 6.9183 7.03477.0485 7.0536 7.1793 12.1183 12.8454 13.066 13.0859 13.0988 13.017823.2544 24.8001 u50 6.918 7.0349 7.0482 7.0535 7.1794 12.1185 12.845813.0655 13.0853 13.0992 13.018 23.2522 24.8226 u51 6.9182 7.035 7.04877.053 7.1801 12.1168 12.8459 13.0656 13.0871 13.0994 13.0168 23.252824.8065 u52 6.918 7.0349 7.0485 7.0531 7.1795 12.1169 12.8459 13.065613.087 13.1016 13.317 25.0373 26.7414 u53 6.9178 7.0346 7.0479 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9.2144 10.1728 17.8043 18.9422 19.2843 19.3034 19.2823 19.436234.7938 37.0074 u74 8.9883 9.1128 9.1275 9.2134 10.1728 17.8046 18.942219.2835 19.3034 19.2808 19.4366 34.7931 37.049 u75 8.9883 9.1126 9.12749.214 10.1726 17.804 18.9418 19.2838 19.3031 19.2822 19.4366 34.792137.0498 u76 8.9879 9.1136 9.127 9.2139 10.1717 17.8043 18.9408 19.28319.3045 19.3161 20.4608 36.6833 39.1338 u77 8.9882 9.1135 9.1271 9.213310.1715 17.8034 18.9414 19.2829 19.3053 19.3159 20.4601 36.6848 39.1318u78 8.9882 9.1132 9.1274 9.2141 10.1715 17.8037 18.9416 19.2832 19.303919.3173 20.4615 36.6846 39.1573 u79 8.9879 9.113 9.1276 9.2149 10.171517.8046 18.9412 19.2829 19.3044 19.3177 20.4603 36.6855 39.1485 u8011.0636 11.2257 11.2138 11.1333 11.7119 19.8603 21.0509 21.4132 21.417921.3639 21.8706 38.7381 41.2799 u81 11.0635 11.2255 11.2144 11.13311.7116 19.8599 21.0506 21.4127 21.4183 21.3649 21.8712 38.7377 41.274u82 11.0637 11.2257 11.2154 11.1333 11.714 19.8602 21.0514 21.41221.4187 21.367 21.8696 38.7374 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37.2756 36.919 38.0893 40.9505 68.5427 72.7465u140 17.8564 18.1475 18.4517 19.3938 21.4901 34.8137 36.7837 37.278137.7322 39.5062 42.4347 70.8714 75.1479 u141 17.8571 18.1476 18.452319.3938 21.4906 34.8127 36.7834 37.2769 37.7329 39.5069 42.4361 70.87275.1592 u142 17.8576 18.1479 18.4516 19.3933 21.4906 34.8145 36.7937.3706 37.7332 39.5058 42.4355 70.871 75.1566 u143 17.8572 18.147818.4511 19.393 21.4902 34.8145 36.7897 37.3711 37.7305 39.5061 42.435970.8711 75.1594 u144 20.2164 20.2868 20.2349 20.9428 23.0809 37.194539.2538 39.6865 39.482 41.0327 43.9712 73.252 77.6014 u145 20.216420.287 20.2356 20.9426 23.0807 37.195 39.2526 39.6866 39.4816 41.03443.9718 73.2505 77.6106 u146 20.2171 20.2869 20.2342 20.9421 23.080737.1962 39.274 39.9285 39.4807 41.0336 43.9717 73.2474 77.6082 u14720.2176 20.2868 20.2369 20.9427 23.0813 37.1952 39.2746 39.9281 39.481441.0328 43.9714 73.2497 77.6298 u148 20.217 20.2859 20.237 20.942523.081 37.1956 39.2739 39.9286 40.6736 42.5141 45.5107 75.6539 80.0702u149 20.2176 20.286 20.2346 20.9428 23.0802 37.1946 39.2732 39.928640.6721 42.5143 45.5113 75.654 80.0995 u150 20.2176 20.286 20.236820.9432 23.0802 37.1942 39.253 39.6881 40.6711 42.5148 45.5116 75.653680.1254 u151 20.2171 20.2859 20.235 20.942 23.0809 37.1952 39.253539.6886 40.672 42.5146 45.5108 75.6539 80.1008 u152 20.4134 20.860721.4443 22.447 24.7 39.6393 41.8477 42.6788 42.3303 44.0788 47.094978.1115 82.6571 u153 20.4138 20.8606 21.4437 22.4469 24.701 39.64 41.84942.6811 42.3299 44.0789 47.0955 78.1106 82.6298 u154 20.4138 20.860921.4429 22.4466 24.7012 39.6412 41.7792 42.1347 42.3305 44.0782 47.094778.1134 82.6678 u155 20.4132 20.8607 21.4436 22.4466 24.7001 39.639941.7774 42.133 42.3312 44.0797 47.0958 78.1145 82.6385 u156 20.413820.8608 21.4442 22.4462 24.7002 39.6454 41.7753 42.132 43.7556 45.626748.6948 80.6014 85.2507 u157 20.4136 20.8605 21.4436 22.446 24.700939.6457 41.7769 42.1336 43.7565 45.6271 48.6963 80.6033 85.2287 u15820.4136 20.8601 21.4444 22.4463 24.7011 39.6446 41.8476 42.6822 43.755345.6272 48.6948 80.6023 85.2642 u159 20.4136 20.8596 21.4451 22.446524.7003 39.645 41.8455 42.6806 43.756 45.628 48.6943 80.603 85.2381 u16022.7291 22.8715 23.1502 24.0705 26.3971 42.1758 44.3495 44.7258 45.403147.2433 50.3384 83.1437 87.8673 u161 22.7294 22.8727 23.1507 24.070426.3968 42.1757 44.3493 44.7254 45.4024 47.243 50.338 83.1448 87.8502u162 22.73 22.8707 23.1507 24.0708 26.3974 42.1754 44.5584 45.741 45.40247.2432 50.3384 83.1435 87.8769 u163 22.7298 22.8702 23.1508 24.071326.3978 42.1756 44.558 45.7422 45.4029 47.2445 50.337 83.1439 87.8927u164 22.7288 22.8717 23.1507 24.0707 26.4013 42.203 44.5579 45.739446.9637 48.8623 52.004 85.7289 90.4885 u165 22.7295 22.8715 23.150724.0709 26.4009 42.2038 44.5571 45.7419 46.9648 48.8638 52.0058 85.730590.5115 u166 22.729 22.8707 23.1498 24.0699 26.4004 42.2042 44.34944.7255 46.9632 48.8622 52.0053 85.7292 90.5583 u167 22.7284 22.870423.1502 24.0703 26.4008 42.2038 44.3487 44.7263 46.9632 48.8632 52.003785.7283 90.5501 u168 23.3002 24.0312 24.7181 25.7297 28.1493 44.781147.4893 49.0867 48.6496 50.5432 53.7116 88.3704 93.1711 u169 23.300324.0317 24.7177 25.7301 28.149 44.7822 47.4905 49.0874 48.6492 50.542153.7115 88.3729 93.1834 u170 23.3001 24.0319 24.7176 25.73 28.148544.7836 46.9655 47.6436 48.6506 50.5416 53.7107 88.375 93.3431 u17123.3002 24.0318 24.7178 25.7296 28.1488 44.7825 46.9643 47.6417 48.650150.543 53.7117 88.3731 93.3278 u172 23.2994 24.0301 24.7179 25.732428.1662 44.884 46.9645 47.6414 50.3142 52.2443 55.4501 91.0631 95.8755u173 23.2995 24.0303 24.7179 25.7328 28.1658 44.8843 46.9654 47.642350.3159 52.2445 55.4497 91.0624 95.8431 u174 23.2997 24.0301 24.717925.7328 28.1663 44.8817 47.4898 49.087 50.3149 52.244 55.4498 91.079796.2453 u175 23.2996 24.0299 24.7182 25.7325 28.1669 44.8822 47.488149.0874 50.3157 52.244 55.4507 91.0806 96.2669 u176 25.5008 25.951526.4839 27.4846 29.9714 47.4569 49.7368 50.924 52.068 54 57.23 93.803598.5959 u177 25.5014 25.9515 26.4825 27.4846 29.9715 47.4576 49.735150.9237 52.0678 54 57.2336 93.8015 98.626 u178 25.5017 25.9508 26.484427.4846 29.9714 47.4561 50.7927 52.6194 52.0687 54.0003 57.2363 93.865199.3573 u179 25.5017 25.9514 26.4829 27.4847 29.9713 47.456 50.791252.6204 52.0688 54.0007 57.2322 93.8657 99.3658 u180 25.5014 25.951626.4861 27.5004 30.0364 47.7567 50.7908 52.6186 53.8366 55.7934 59.063196.5768 101.5264 u181 25.5028 25.9505 26.4855 27.5001 30.0362 47.754350.792 52.6204 53.8379 55.7949 59.0487 96.5759 101.5192 u182 25.50325.9503 26.4853 27.5 30.0364 47.7547 49.7345 50.9223 53.8375 55.794759.0513 96.744 102.7774 u183 25.5017 25.9503 26.4848 27.5001 30.036647.756 49.7351 50.923 53.8375 55.7945 59.0654 96.7471 102.758 u18426.7564 27.6499 28.2924 29.3043 31.8445 50.2126 54.481 56.352 55.679957.6402 60.9066 99.3737 104.7895 u185 26.7557 27.6505 28.2926 29.304631.8444 50.2112 54.482 56.3524 55.6794 57.6402 60.9514 99.3735 104.784u186 26.756 27.6502 28.2928 29.3051 31.845 50.2115 52.8879 54.493755.6799 57.6424 60.9527 99.7791 106.3724 u187 26.7572 27.6495 28.292629.3047 31.8451 50.2119 52.8889 54.4927 55.6801 57.6445 60.9074 99.7778106.3917 u188 26.7547 27.6507 28.3062 29.37 32.0502 50.946 52.887354.4931 57.5635 59.5304 62.9105 102.2392 108.3364 u189 26.7551 27.651528.3063 29.3703 32.0499 50.9478 52.8862 54.4933 57.5626 59.53 62.7907102.2389 108.3192 u190 26.7555 27.6518 28.3063 29.3699 32.0493 50.947354.4811 56.3535 57.5625 59.5426 62.7919 103.0672 110.0782 u191 26.755727.6508 28.3063 29.3696 32.0496 50.9471 54.4777 56.3517 57.5619 59.542162.9118 103.0709 110.098 u192 28.8967 29.6329 30.2211 31.1985 33.787853.2472 56.5129 58.3201 59.5158 61.4692 64.6982 105.3423 112.0229 u19328.8954 29.6343 30.221 31.1988 33.7878 53.2474 56.5126 58.3198 59.51561.47 64.9878 105.3399 112.0215 u194 28.8984 29.6333 30.2209 31.197733.7875 53.2471 58.4305 60.3284 59.518 61.5083 64.9887 106.6962 113.9226u195 28.8957 29.6335 30.2207 31.1976 33.788 53.2469 58.432 60.329459.5174 61.51 64.6986 106.6951 113.9457 u196 28.8964 29.6482 30.288631.4137 34.3072 54.6317 58.4322 60.3288 61.5225 63.4448 67.26 108.8201115.9569 u197 28.8963 29.6491 30.2889 31.4126 34.306 54.6309 58.429360.3278 61.5228 63.4457 66.6604 108.8239 115.9373 u198 28.894 29.647930.289 31.4145 34.3064 54.6318 56.5113 58.3212 61.5361 63.5607 66.6623110.5569 117.9697 u199 28.8976 29.6487 30.2896 31.4154 34.3076 54.631856.5111 58.321 61.5357 63.5603 67.2615 110.5568 117.968 u200 30.838531.6761 32.2269 33.1745 35.9425 56.8147 62.6807 64.6275 63.5938 65.451168.8078 112.6399 120.0732 u201 30.8381 31.6768 32.2268 33.1746 35.942156.8143 62.6818 64.6076 63.5943 65.4502 69.7793 112.6406 120.0877 u20230.8377 31.6763 32.227 33.1739 35.9427 56.8128 60.5371 62.4377 63.643465.7446 69.7799 114.58 122.2273 u203 30.8383 31.676 32.2271 33.174135.9422 56.8135 60.5377 62.4326 63.6414 65.7458 68.808 114.5829 122.2176u204 30.8669 31.7659 32.4737 33.7422 36.9479 58.7337 60.5375 62.433265.7106 67.522 72.4667 116.7006 124.3592 u205 30.8648 31.7665 32.473233.7425 36.9485 58.7335 60.5371 62.4378 65.711 67.5211 71.2356 116.7014124.3665 u206 30.864 31.767 32.4725 33.7413 36.9488 58.7342 62.681264.6057 65.8604 68.1558 71.236 118.7805 126.5951 u207 30.8655 31.766432.473 33.7407 36.9481 58.7348 62.6782 64.6256 65.861 68.1547 72.4679118.7799 126.6084 u208 33.0856 33.8573 34.3557 35.4122 38.511 60.948564.961 66.8665 67.8719 69.8016 73.9063 120.9783 128.8537 u209 33.085333.8583 34.3563 35.4118 38.5104 60.9502 64.9502 66.9393 67.8724 69.802875.282 120.979 128.8255 u210 33.0852 33.8597 34.3549 35.4117 38.509460.9512 67.3556 69.1826 68.2597 70.8585 75.2825 123.1866 131.1588 u21133.0862 33.8583 34.356 35.411 38.5111 60.9498 67.3087 69.4073 68.260170.8586 73.9069 123.1854 131.1615 u212 33.2214 34.1824 35.0169 36.513139.9201 63.2019 67.3081 69.4075 70.1446 72.4123 78.2505 125.4882133.5366 u213 33.2217 34.1828 35.0176 36.5134 39.9208 63.1955 67.35569.1817 70.1445 72.4125 76.7655 125.4847 133.5237 u214 33.2237 34.182235.0165 36.5124 39.9194 63.1964 64.9502 66.9385 70.956 73.7621 76.7652127.8281 136.0317 u215 33.2235 34.1819 35.0172 36.5121 39.9192 63.200364.9603 66.8654 70.9565 73.7626 78.2503 127.8291 136.0114 u216 35.44536.2138 36.8228 38.1341 41.5374 65.6006 72.2936 75.2914 72.7133 75.315979.8088 130.2594 138.5627 u217 35.4434 36.2154 36.823 38.134 41.538465.6352 72.7658 74.1616 72.7133 75.3153 81.3985 130.2599 138.5417 u21835.443 36.2148 36.8226 38.1337 41.5337 65.635 69.7645 72.1447 73.991676.8318 81.398 132.7503 141.24 u219 35.4452 36.2154 36.822 38.133541.5332 65.6034 69.9292 71.5687 73.9915 76.8334 79.8097 132.7523141.1228 u220 35.9446 37.0809 38.1143 39.6668 43.2259 68.2437 69.9371.5669 75.6828 78.4548 84.7489 135.3208 143.9764 u221 35.9439 37.080738.1159 39.6739 43.2253 68.1096 69.7646 72.1413 75.6824 78.4533 83.05135.3322 143.7174 u222 35.9415 37.0793 38.1138 39.6751 43.1935 68.109772.7645 74.1629 77.2562 80.1038 83.0502 137.9532 146.9884 u223 35.939937.0795 38.1142 39.6685 43.1934 68.2451 72.2929 75.2906 77.2558 80.102584.7445 138.0018 146.3707 u224 38.1421 39.0748 39.9061 41.4312 45.092170.724 76.0497 77.1971 78.9949 81.8321 86.5172 140.6489 150.2997 u22538.1407 39.0737 39.9051 41.3874 45.0917 71.148 75.0027 78.8149 78.993581.8308 88.3057 140.7959 149.1778 u226 38.1387 39.0729 39.9136 41.387444.9563 71.1475 79.8563 80.725 80.7524 83.6178 88.3586 143.3857 153.9366u227 38.1393 39.072 39.9138 41.4318 44.9577 70.7252 78.1693 82.631380.752 83.6106 86.5021 143.7715 152.3383 u228 39.3811 40.6933 41.680743.1806 47.2136 74.5365 78.1688 82.6346 82.615 85.4919 92.4479 146.2133157.7208 u229 39.3797 40.6954 41.6813 43.3578 47.2147 73.5145 79.854980.7237 82.6175 85.4642 90.1531 147.0624 155.918 u230 39.383 40.717741.7473 43.3615 46.7928 73.5134 75.0026 78.8136 84.5431 87.468 90.3172149.3221 161.6712 u231 39.3822 40.7174 41.7472 43.1824 46.7917 74.536876.0486 77.1971 84.5564 87.3728 92.0413 150.7556 159.7367 u232 41.586442.737 43.629 45.6178 49.8016 76.7947 86.3111 91.7814 86.5573 89.600294.8545 152.8896 165.8723 u233 41.5862 42.7351 43.6295 45.0949 49.786678.5611 88.8104 89.0424 86.6142 89.3315 96.3559 154.7376 163.7698 u23441.6242 42.8512 43.8894 45.0964 48.8317 78.5612 81.9544 86.8512 88.631491.9867 97.5297 156.866 170.3772 u235 41.6217 42.8509 43.8899 45.618948.8326 76.7942 84.0476 84.681 88.8158 91.3653 94.0545 158.9374 168.0686u236 43.6586 44.8534 45.73 47.2945 56.2922 83.0754 84.0414 84.690490.773 94.7231 103.4371 161.1551 175.1357 u237 43.6584 44.8547 45.732248.4058 55.1603 80.8156 81.9552 86.8115 91.2635 93.6365 98.9928 163.3988172.7418 u238 43.91 45.3023 46.474 48.4076 51.4219 80.8115 88.674989.1885 93.1011 97.712 100.3833 165.7558 180.196 u239 43.9111 45.301146.474 47.2943 51.4466 83.1093 86.3407 91.3499 94.1018 96.2886 101.9016168.1813 177.6286 u240 46.0819 47.3076 48.295 51.6846 52.6019 85.52793.8045 94.7999 95.8386 103.2027 106.7386 170.7183 185.5392 u241 46.084847.3029 48.2917 50.0756 53.0145 88.5886 91.5754 96.7404 97.3072 99.3683108.4985 173.352 182.8435 u242 46.875 48.4368 49.7504 50.0677 54.515688.0935 100.855 102.1953 99.0435 100.7888 110.3385 176.0937 191.2394u243 46.8669 48.4418 49.7745 51.755 57.1194 85.6786 98.6951 104.3252100.7888 104.8564 105.0578 178.9503 188.3099 u244 49.0907 50.465451.6106 53.482 58.5488 94.3568 96.9609 106.5724 102.6686 106.7538118.5975 181.9285 201.4817 u245 49.0876 50.5103 51.7362 56.187 59.687192.0944 103.0735 100.2446 104.6415 113.0328 112.264 185.0249 198.2276u246 50.8187 52.3785 53.5473 55.4438 61.0587 90.9153 91.1447 98.3088106.7469 110.8313 114.2781 188.2473 195.0877 u247 50.9711 52.6554 54.01453.7502 62.383 96.3402 94.8234 93.8297 113.8639 108.735 116.388 191.6011204.8098 u248 53.1308 54.6369 55.8333 61.0935 63.9382 98.7255 110.9823109.8671 111.3485 116.2929 128.5722 195.0998 220.3335 u249 53.672755.4539 56.9776 59.2965 65.5845 101.2692 108.1322 112.4678 108.9785124.0975 125.8846 198.7608 208.9816 u250 55.8554 57.4983 58.8538 57.871667.4378 104.0613 105.5088 115.268 120.9644 121.3467 123.3387 207.3405212.6536 u251 57.3141 59.2853 60.7781 63.0654 69.4919 107.1332 114.0763118.2761 124.0148 118.7481 120.9102 203.3115 216.39 u252 59.7306 61.602463.0444 65.3044 71.7827 110.5139 117.4441 121.5172 117.5046 127.78131.8728 212.2402 229.8116 u253 62.446 64.281 65.6351 67.8256 74.338114.2433 125.8827 125.0262 127.8356 130.9128 134.9058 216.7609 225.4612u254 65.7278 67.4355 68.6262 70.6915 77.2123 118.4101 121.8065 128.8876131.439 134.3281 138.1853 221.6351 235.0857 u255 69.7535 71.2292 72.177574.0527 80.5656 123.224 131.1028 133.2942 135.5132 138.1588 141.8506227.06 240.4439i) 1048576-QAM/1024-PAM for a Non-Fading Channel

SNR 0 1 2 3 4 5 6 7 8 9 10 u1 1.0002 1 0.9999 0.9999 1.0002 0.99961.0001 0.9993 0.9995 1 0.9998 u2 1.0004 1 0.9998 0.9999 1.0005 0.99921.0003 0.9982 0.9985 0.9963 0.999 u3 1.0007 1.0001 0.9998 0.9999 1.00070.9989 1.0008 0.9992 0.999 0.9959 0.9988 u4 1.0008 1 0.9995 0.99981.0009 0.9986 1.001 0.9965 0.9927 0.9921 0.9939 u5 1.0011 1 0.99940.9998 1.0011 0.9982 1.002 0.9958 0.9921 0.9921 0.9936 u6 1.0012 1.00010.9994 0.9998 1.0014 0.998 1.002 0.9962 0.9929 0.9954 0.994 u7 1.00161.0002 0.9993 0.9998 1.0018 0.9978 1.0026 0.9956 0.9937 0.995 0.9938 u81.0013 0.9995 0.9986 0.9996 1.0019 0.9974 1.0029 0.9887 0.9727 0.97360.9874 u9 1.0015 0.9995 0.9985 0.9995 1.0021 0.997 1.0028 0.9871 0.97210.9736 0.9872 u10 1.0018 0.9995 0.9984 0.9994 1.0024 0.9966 1.00310.9865 0.9709 0.9698 0.9864 u11 1.002 0.9996 0.9984 0.9994 1.0026 0.99631.0037 0.9866 0.9716 0.9695 0.9863 u12 1.0023 0.9998 0.9984 0.99941.0029 0.996 1.004 0.9868 0.978 0.9728 0.9908 u13 1.0026 0.9999 0.99830.9993 1.0031 0.9957 1.0043 0.9861 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151.536 168.5033 u469 45.4984 49.798 78.3199 81.7436 86.503388.4291 91.1957 93.9086 151.5386 168.4994 u470 45.4972 49.7981 78.327383.8017 86.4712 88.2699 91.7357 93.9109 157.4443 162.0943 u471 45.497649.7981 78.3238 83.8072 86.4722 88.2701 91.7341 93.2111 157.4372162.0979 u472 47.1812 51.4008 80.5853 86.052 88.8102 90.8379 93.4148102.3437 159.6629 178.0281 u473 47.1793 51.3999 80.5784 86.0775 88.808590.8395 93.4126 100.8371 159.7353 178.0888 u474 47.1792 51.3996 80.577888.3989 88.6874 90.4077 94.418 100.8385 161.4906 170.7864 u475 47.177551.3998 80.5826 88.5045 88.6874 90.407 94.4168 102.3437 162.0578170.7885 u476 48.2602 52.8027 82.8266 88.5079 91.351 93.6197 96.001797.9904 164.329 173.1246 u477 48.2589 52.8033 82.8247 88.399 91.351793.6216 96.001 99.3405 166.9644 173.1339 u478 48.2571 52.8089 82.863586.0761 90.9752 92.7009 97.3717 99.3403 166.8286 175.5452 u479 48.257852.8079 82.8658 86.0498 90.9768 92.7021 97.3718 97.9893 164.9195175.5667 u480 49.9204 54.4608 85.2749 94.3572 94.308 96.7916 98.9623109.0638 171.9601 183.1706 u481 49.9207 54.4594 85.2789 93.4722 94.30596.7938 98.9639 107.3125 169.4261 183.561 u482 49.9267 54.4959 85.409191.2062 93.4157 95.3759 100.5473 107.2919 169.3906 185.8604 u483 49.929554.4958 85.4157 90.8593 93.4156 95.3754 100.5491 109.138 172.0146186.6658 u484 51.5221 56.1812 87.8379 90.8599 97.7921 100.2475 102.245103.9362 174.6048 188.8092 u485 51.5246 56.181 87.8408 91.2098 97.7919100.2473 102.2485 105.5795 177.7215 190.1516 u486 51.5879 56.336788.2852 93.4714 96.2548 98.5286 104.0024 105.5764 177.2994 180.5749 u48751.5863 56.337 88.2862 94.3565 96.2546 98.5303 104.0187 103.9358174.7609 180.7371 u488 53.3161 58.0275 90.6272 96.5321 106.0663 104.0424105.8492 117.3113 183.2688 207.205 u489 53.3156 58.0272 90.6288 98.1431105.9258 104.0839 105.9014 115.8266 181.0581 201.9648 u490 53.560358.5022 91.7549 100.2597 99.7346 102.1054 107.7543 114.8657 180.109192.1819 u491 53.5598 58.5013 91.7452 102.7452 99.7353 102.1144 107.9239118.618 184.8946 193.9278 u492 55.2561 60.1408 94.0274 102.094 101.6902108.1702 109.7293 110.8906 187.0507 195.9463 u493 55.2536 60.140194.0225 100.3662 101.6823 108.5941 110.1842 113.2987 189.0814 197.9263u494 55.9575 61.1933 95.9591 98.1398 103.7922 106.0702 111.8828 112.7799191.2342 200.1039 u495 55.9545 61.193 95.9578 96.5259 103.7559 106.2142112.8128 111.1046 193.4234 205.0979 u496 57.6385 62.8176 98.2729110.7233 111.6839 113.1487 114.4232 130.5814 195.7412 217.4963 u49757.642 62.8281 98.3185 112.2847 110.6768 114.6195 115.7969 132.6632198.1371 214.7692 u498 59.0042 64.3876 100.6974 107.626 115.2945110.4487 117.4144 126.718 200.6614 223.3043 u499 59.0342 64.465 100.9143108.7795 113.6476 111.3842 119.0583 128.5997 203.2991 220.3407 u50060.7329 66.1457 103.2898 104.8265 119.3173 120.0971 120.8309 120.1201206.0702 229.6263 u501 60.8673 66.4305 103.9738 105.8718 117.3087130.1909 127.7652 124.9348 208.9752 226.3983 u502 62.5426 68.0764106.2703 114.3264 108.6353 116.3941 129.9928 123.2466 212.0266 212.1517u503 63.0233 68.845 107.8059 116.3532 108.2046 118.2137 122.6547 121.632215.2249 209.6442 u504 64.7063 70.4884 110.0966 118.6444 130.9001122.984 134.8738 137.7682 218.5842 236.4769 u505 65.8405 71.9292112.3906 121.1165 122.8929 125.2188 132.3583 135.4531 222.1134 244.6645u506 67.5824 73.7057 115.0313 123.8409 125.3324 127.6202 125.6912140.7453 225.8235 240.8179 u507 69.4139 75.665 117.9552 126.8307128.0094 133.5832 137.548 143.3382 229.737 232.9769 u508 71.5481 77.8744121.1796 130.1067 134.716 136.5634 140.4019 146.0965 233.8787 249.6594u509 73.9871 80.3612 124.7913 133.7124 138.147 139.7863 143.479 149.0639238.2892 253.9707 u510 76.7941 83.1813 128.8735 137.7296 141.9513143.3296 146.8374 152.2948 243.1015 264.3589 u511 80.1201 86.4858133.6086 142.366 146.2886 147.35 150.6362 155.922 248.5007 259.1528

Obviously, numerous modifications and variations of the presentdisclosure are possible in light of the above teachings. It is thereforeto be understood that within the scope of the appended claims, thedisclosure may be practiced otherwise than as specifically describedherein (e.g., if the NUC position vectors are rounded to a smallernumber of digits).

In the claims, the word “comprising” does not exclude other elements orsteps, and the indefinite article “a” or “an” does not exclude aplurality. A single element or other unit may fulfill the functions ofseveral items recited in the claims. The mere fact that certain measuresare recited in mutually different dependent claims does not indicatethat a combination of these measures cannot be used to advantage.

In so far as embodiments of the disclosure have been described as beingimplemented, at least in part, by software-controlled data processingapparatus, it will be appreciated that a non-transitory machine-readablemedium carrying such software, such as an optical disk, a magnetic disk,semiconductor memory or the like, is also considered to represent anembodiment of the present disclosure. Further, such a software may alsobe distributed in other forms, such as via the Internet or other wiredor wireless telecommunication systems.

A circuit that may be used for implementing one or more of the elementsof the claimed apparatus is a structural assemblage of electroniccomponents including conventional circuit elements, integrated circuitsincluding application specific integrated circuits, standard integratedcircuits, application specific standard products, and field programmablegate arrays. Further a circuit includes central processing units,graphics processing units, and microprocessors which are programmed orconfigured according to software code. A circuit does not include puresoftware, although a circuit includes the above-described hardwareexecuting software.

Any reference signs in the claims should not be construed as limitingthe scope.

The invention claimed is:
 1. A coding and modulation apparatus,comprising: an encoder configured to encode input data into cell words;a modulator configured to modulate the cell words into constellationvalues of a non-uniform constellation (NUC); and a converter thatconverts the constellation values into one or more data streams, whereinthe NUC is a 1024-QAM constellation, the modulator is configured to use,based on a total number M constellation points of the NUC, the NUCdefined by a constellation position vector wherein u_(1 . . . v),wherein v=(sqrt(M)/2)−1: u₁ = 1.0003 u₂ = 1.0149 u₃ = 1.0158 u₄ = 2.6848u₅ = 2.6903 u₆ = 2.882 u₇ = 2.8747 u₈ = 4.7815 u₉ = 4.7619 u₁₀ = 5.5779u₁₁ = 5.6434 u₁₂ = 7.3854 u₁₃ = 7.8797 u₁₄ = 9.635 u₁₅ = 11.7874,

M=1024, and each constellation position of the constellation positionvector describes five-bit labels for both real and imaginary componentsof the NIX according to the following: Constellation mapping for realpart of 1024-QAM Y_(0,q) 1 1 1 1 1 1 1 1 1 y_(2,q) 0 0 0 0 0 0 0 0 1y_(4,q) 0 0 0 0 1 1 1 1 1 y_(6,q) 0 0 1 1 1 1 0 0 0 y_(8,q) 0 1 1 0 0 11 0 0 Re(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −u₁₅ −u₁₄ −u₁₃ −u₁₂−u₁₁ −u₁₀ −u₉ −u₈ −u₇ Y_(0,q) 0 0 0 0 0 0 0 0 0 y_(2,q) 1 1 1 1 1 1 1 10 y_(4,q) 0 0 0 0 1 1 1 1 1 y_(6,q) 0 0 1 1 1 1 0 0 0 y_(8,q) 0 1 1 0 01 1 0 0 Re(z_(q)) 1 3 5 7 9 11 13 15 17 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈Y_(0,q) 1 1 1 1 1 1 1 y_(2,q) 1 1 1 1 1 1 1 y_(4,q) 1 1 1 0 0 0 0y_(6,q) 0 1 1 1 1 0 0 y_(8,q) 1 1 0 0 1 1 0 Re(z_(q)) −13 −11 −9 −7 −5−3 −1 Uniform −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUC Y_(0,q) 0 0 0 0 0 0 0y_(2,q) 0 0 0 0 0 0 0 y_(4,q) 1 1 1 0 0 0 0 y_(6,q) 0 1 1 1 1 0 0y_(8,q) 1 1 0 0 1 1 0 Re(z_(q)) 19 21 23 25 27 29 31 Uniform u₉ u₁₀ u₁₁u₁₂ u₁₃ u₁₄ u₁₅ NUC

Constellation mapping for imaginary part of 1024-QAM y_(1,q) 1 1 1 1 1 11 1 1 y_(3,q) 0 0 0 0 0 0 0 0 1 y_(5,q) 0 0 0 0 1 1 1 1 1 y_(7,q) 0 0 11 1 1 0 0 0 y_(9,q) 0 1 1 0 0 1 1 0 0 Im(z_(q)) −31 −29 −27 −25 −23 −21−19 −17 −15 −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ y_(1,q) 0 0 0 0 00 0 0 0 y_(3,q) 1 1 1 1 1 1 1 1 0 y_(5,q) 0 0 0 0 1 1 1 1 1 y_(7,q) 0 01 1 1 1 0 0 0 y_(9,q) 0 1 1 0 0 1 1 0 0 Im(z_(q)) 1 3 5 7 9 11 13 15 171 u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ y_(1,q) 1 1 1 1 1 1 1 y_(3,q) 1 1 1 1 1 1 1y_(5,q) 1 1 1 0 0 0 0 y_(7,q) 0 1 1 1 1 0 0 y_(9,q) 1 1 0 0 1 1 0Im(z_(q)) −13 −11 −9 −7 −5 −3 −1 Uniform −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUCy_(1,q) 0 0 0 0 0 0 0 y_(3,q) 0 0 0 0 0 0 0 y_(5,q) 1 1 1 0 0 0 0y_(7,q) 0 1 1 1 1 0 0 y_(9,q) 1 1 0 0 1 1 0 Im(z_(q)) 19 21 23 25 27 2931 Uniform u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC


2. The coding and modulation apparatus according to claim 1, wherein theNUC further includes a constellation position u₀ with a value of
 1. 3.The coding and modulation apparatus according to claim 2, wherein thepositions u_(0 . . .) u₁₅ define cell words representing binary inputdata in a constellation.
 4. The coding and modulation apparatusaccording to claim 3, wherein each position of u_(0 . . .) u₁₅represents respectively a positive and negative real and imaginary valuewhich, when plotted against each other on a real and imaginary axis,represent positions of 1024 bit labels, the bit labels corresponding tothe cell words.
 5. The coding and modulation apparatus according toclaim 4, wherein each cell word comprises 10 bits.
 6. The coding andmodulation apparatus according to claim 4, wherein a bit labelcorresponding to one constellation position on the real and imaginaryaxis differs by only one bit from a bit label for an adjacentconstellation position.
 7. The coding and modulation apparatus accordingto claim 1, wherein the encoder is a forward error correction codeencoder.
 8. The coding and modulation apparatus according to claim 2,wherein the modulator is configured to use the NUC so that, when poweris normalized, the NUC is represented by a constellation position vectoru_(0 . . . v): u₀ = 0.1275 u₁ = 0.1276 u₂ = 0.1294 u₃ = 0.1295 u₄ =0.3424 u₅ = 0.3431 u₆ = 0.3675 u₇ = 0.3666 u₈ = 0.6097 u₉ = 0.6072 u₁₀ =0.7113 u₁₁ = 0.7196 u₁₂ = 0.9418 u₁₃ = 1.0048 u₁₄ = 1.2286 u₁₅ = 1.5031.


9. The coding and modulation apparatus as claimed in claim 8, whereineach position of u_(0 . . .) u₁₅ represents respectively a positive andnegative real and imaginary value which, when plotted against each otheron a real and imaginary axis, represent positions of 1024 bit labels,the bit labels corresponding to the cell words.
 10. A transmissionapparatus, comprising: the coding and modulation apparatus as recited inclaim 1; and a transmitter configured to transmit the one or more datastreams.
 11. The transmission apparatus of claim 10, wherein thetransmitter is configured to transmit the one or more data streams forterrestrial delivery having fading channels.
 12. A communicationssystem, comprising: one or more of the transmission apparatus as claimedin claim 10; and one or more receiving apparatus.
 13. A coding andmodulation method, comprising: encoding input data into cell words;modulating, by circuitry, the cell words into constellation values of anon-uniform constellation (NUC); and converting said constellationvalues into one or more data streams, wherein the NUC constellation is a1024-QAM constellation, in the modulating, the circuitry uses, based ona total number M constellation points of the NUC, the NUC defined by aconstellation position vector u_(1 . . . v), wherein v=(sqrt(M)/2)−1: u₁= 1.0003 u₂ = 1.0149 u₃ = 1.0158 u₄ = 2.6848 u₅ = 2.6903 u₆ = 2.882 u₇ =2.8747 u₈ = 4.7815 u₉ = 4.7619 u₁₀ = 5.5779 u₁₁ = 5.6434 u₁₂ = 7.3854u₁₃ = 7.8797 u₁₄ = 9.635 u₁₅ = 11.7874, and

M=1024, and each constellation position of the constellation positionvector describes five-bit labels for both real and imaginary componentsof the NUC according to the following: Constellation mapping for realpart of 1024-QAM Y_(0,q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 y_(2,q) 0 0 0 00 0 0 0 1 1 1 1 1 1 1 1 y_(4,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6,q)0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0Re(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂−u₁ −1 NUC Y_(0,q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2,q) 1 1 1 1 1 1 11 0 0 0 0 0 0 0 0 y_(4,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(6,q) 0 0 11 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0Re(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1 u₁ u₂ u₃u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC

Constellation mapping for imaginary part of 1024-QAM y_(1,q) 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 y_(3,q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(5,q) 0 00 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0y_(9,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −31 −29 −27 −25 −23−21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁−u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUC y_(1,q) 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 y_(3,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(5,q) 0 0 0 01 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9,q)0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 2325 27 29 31 Uniform 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅NUC


14. The coding and modulation method according to claim 13, furthercomprising modifying the NUC to further include a constellation positionu₀ with a value of
 1. 15. The coding and modulation method according toclaim 14, wherein in the modulating, the circuitry uses the NIX so that,when power is normalized, the NUC is represented by a constellationposition vector u_(0 . . . v): u₀ = 0.1275 u₁ = 0.1276 u₂ = 0.1294 u₃ =0.1295 u₄ = 0.3424 u₅ = 0.3431 u₆ = 0.3675 u₇ = 0.3666 u₈ = 0.6097 u9 =0.6072 u₁₀ = 0.7113 u₁₁ = 0.7196 u₁₂ = 0.9418 u₁₃ = 1.0048 u₁₄ = 1.2286u₁₅ = 1.5031.


16. A non-transitory computer readable medium including computer programinstructions which, when executed by a computer including the circuitry,causes the computer to perform the coding and modulation method of claim13.
 17. A receiving method, comprising demodulating cell words modulatedand encoded according to the coding and modulation method of claim 13.18. A decoder and demodulation apparatus, comprising: a converter thatconverts one or more data streams into constellation values of anon-uniform constellation (NUC); a demodulator configured to demodulatethe constellation values into cell words; and a decoder configured todecode cell words into input data, wherein the NUC is a 1024-QAMconstellation, the demodulator is configured to use, based on a totalnumber M constellation points of the NUC, the NUC is defined by aconstellation position vector u_(1 . . . v), v=(sqrt(M)/2)−1: u₁ =1.0003 u₂ = 1.0149 u₃ = 1.0158 u₄ = 2.6848 u₅ = 2.6903 u₆ = 2.882 u₇ =2.8747 u₈ = 4.7815 u₉ = 4.7619 u₁₀ = 5.5779 u₁₁ = 5.6434 u₁₂ = 7.3854u₁₃ = 7.8797 u₁₄ = 9.635 u₁₅ = 11.7874,

M=1024, and each constellation position of the constellation positionvector describes five-bit labels for both of real and imaginarycomponents of the NIX according to the following: Constellation mappingfor real part of 1024-QAM Y_(0,q) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1y_(2,q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(4,q) 0 0 0 0 1 1 1 1 1 1 1 10 0 0 0 y_(6,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 00 1 1 0 0 1 1 0 Re(z_(q)) −31 −29 −27 −25 −23 −21 −19 −17 −15 −13 −11 −9−7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁ −u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅−u₄ −u₃ −u₂ −u₁ −1 NUC Y_(0,q) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 y_(2,q) 11 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(4,q) 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0y_(6,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(8,q) 0 1 1 0 0 1 1 0 0 1 1 00 1 1 0 Re(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Uniform 1u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅ NUC

Constellation mapping for imaginary part of 1024-QAM y_(1,q) 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 y_(3,q) 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 y_(5,q) 0 00 0 1 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0y_(9,q) 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) −31 −29 −27 −25 −23−21 −19 −17 −15 −13 −11 −9 −7 −5 −3 −1 Uniform −u₁₅ −u₁₄ −u₁₃ −u₁₂ −u₁₁−u₁₀ −u₉ −u₈ −u₇ −u₆ −u₅ −u₄ −u₃ −u₂ −u₁ −1 NUC y_(1,q) 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 y_(3,q) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 y_(5,q) 0 0 0 01 1 1 1 1 1 1 1 0 0 0 0 y_(7,q) 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 y_(9,q)0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 Im(z_(q)) 1 3 5 7 9 11 13 15 17 19 21 2325 27 29 31 Uniform 1 u₁ u₂ u₃ u₄ u₅ u₆ u₇ u₈ u₉ u₁₀ u₁₁ u₁₂ u₁₃ u₁₄ u₁₅NUC


19. The decoder and demodulation apparatus according to claim 18,wherein the NUC further includes a constellation position u₀ with avalue of 1, and the demodulator is configured to use the NUC so that,when power is normalized, the NUC is represented by a constellationposition vector u_(0 . . . v): u₀ = 0.1275 u₁ = 0.1276 u₂ = 0.1294 u₃ =0.1295 u₄ = 0.3424 u₅ = 0.3431 u₆ = 0.3675 u₇ = 0.3666 u₈ = 0.6097 u9 =0.6072 u₁₀ = 0.7113 u₁₁ = 0.7196 u₁₂ = 0.9418 u₁₃ = 1.0048 u₁₄ = 1.2286u₁₅ = 1.5031.


20. The receiver apparatus according to claim 19, wherein each positionof u_(0 . . .) u₁₅ represents respectively a positive and negative realand imaginary value which, when plotted against each other on a real andimaginary axis, represent positions of 1024 bit labels, the bit labelscorresponding to the cell words.
 21. A receiver apparatus, comprising:the decoder and demodulation apparatus according to claim 18; and areceiver configured to receive the one or more data streams.
 22. Thereceiver apparatus according to claim 21, wherein the receiver isconfigured to receive the one or more data streams for terrestrialdelivery having fading channels.